Cydia install method may very according to your iOS version and device model. So you must choose correct Cydia install according to those factors. Go to Cydia page and get most compatibale Cydia install method according to your iOS version and device model.
Pangu logo
Pangu Links
(1) Connect your device to the computer. It will detect your device as iOS 9.3 beta
(2) The process will start. Then Pangu app icon will create on your springboard.
Don’t tap it at this time.
(3) Then the device will reboot, and the process will continue.
(4) Ok. Now you have to open the Pangu app.
(6) Then tap the home button and open Pangu app again.
(7) iOS 9.3 beta jailbreak process will continue. Then your device will restart again.
(8) Finally red “jailbreak complete” message will display on the Pangu tool.
(10) Connect your iOS 9.3 beta device to computer

Backup device data before starting process
Don't tap it at this time
pangu app access your messages
pangu 9.3 jailbreak tool
cydia preparing file system
cydia 1.1.26
Copyright @ 2016
(5) You must allow Pangu app to access to your messages.

Step guide to downgrade iOS 9.3.4 and Jailbreak

Important - You must have an iOS 9.3.3 Backup on your computer or iClould, Don't set the iOS 9.3.4 backup as the last backup option.
Step 1) Download the iOS 9.3.3 version to your computer according to your device model.

There is no any option to download iOS 9.3.3 through iTunes if you have updated your device to iOS 9.3.4
Step 2) Connect your device to your computer (Using a cable) and open the iTunes.

We recommend to upgrade your iTunes to the latest version before start this step
Step 3) Click the device icon. Check top right corner of iTunes to find this icon
Check iOS 9.3.4 version
Step 4) This is the most important step.
Hold Shift (Windows users) or Option key /Alt key (Mac users) on your keyboard and Click the "Check for updates" button. Not the "Restore iPhone/iPad" button.
Downgrade iOS 9.3.4
Step 5) Then select the iOS 9.3.3 IPSW file and start the upgrading. It takes few minutes to complete the upgrade.
iOS 9.3.4 Jailbreak by Luca
The hacker just participated in the DefCon hacking conference. But, He never the Pangu team'
luca tweet pangu
Download the Pangu Jailbreak tool from the following link. (Only for Windows users). Mac user follows the iOS 9.3.3 Jailbreak guide from here
Please visit this page from your computer to download the tool
Double click and Open it,  Make sure that you have already backed up your device, turned off Touch ID/Passcode and disable "Find my iPhone"
pangu tool for iOS 9.3.4
Plug your device into your Windows computer and click Generate button to generate the Signed IPA according to your device model.
Cydia Impactor
Then Cydia Impactor (Freeware) will download automatically to your computer. Click open button to open the Cydia Impactor.
Cydia Impactor
You can find the generated "IPA" file on your desktop. Drag it to the Cydia Impactor.
IPA  file on your desktop
Cydia Impactors shows an Error message. Skip it and sign to your Apple user account through Cydia Impactor.
Error message for apple
Cydia Impactor installs the "Pangu Jailbreak" app to your device. Now close the Cydia Impactor
Pangu Jailbreak for iOS 9.3.4
Don't open the Pangu app at this time. Open Settings, General and device management. Make the Pangu app profile as the "Trust."
Trust Pangu app profile
Then Open the Pangu app to start the Jailbreak process. It installs the fully functional Cydia to your device.
Pangu app to start the Jailbreak
Cydia to your device

iOS 9.3.4/9.3.5 Jailbreak and Cydia installation

Windows/Mac tool based Jailbreak (Full Jailbreak)

A complete guide to Jailbreak iOS 9.3.4 and iOS 9.3.5, You can download Jailbreak tools according to your Computer (Windows or Mac). You can install Cydia after the Jailbreak process
Online Partial Jailbreak - This method is super easier than below method. You can Jailbreak your iOS device just visiting this web page from your iOS device. However, You cannot install full functional Cydia using this method.

Semi Jailbreak process for iOS 9.3 - iOS 9.3.4 , iOS 9.3.5

Semi Jailbreak version 1.2 is compatible with iOS 9.3 - iOS 9.3.5. This process is a risk-free/reversible process. You can do Semi Jailbreak from our website or their official website.
Step 1)  Visit this web page from your iOS device. Your iOS version must be iOS 9.3 - iOS 9.3.5
Step 2) Tap the "Jailbreak iOS 9.3 - 9.3.5" button
Step3) It checks your system compatibility. You can continue if you are iOS 9.3 - iOS 9.3.5 user.
Step 4) Click the Agree button to start the Semi Jailbreak process.
Step 5) You can install the Semi Jailbreak app after the process. Please wait until Semi Jailbreak app install menu appear.
Step 6) Tap the "install" link ( above - right side corner) to install the Semi Jailbreak app
Step 7) You can use this Semi Jailbreak app to install the Cydia and more Jailbreak App stores.

iOS 9.3.4 Windows Jailbreak guide.

iOS 9.3, iOS 9.3.1, iOS 9.3.2 and iOS 9.3.3 Jailbreak methods are almost same. However, Don't upgrade to iOS 9.3.4 if you are iOS 9.3, 9.3.1, 9.3.2 and 9.3.3.
Visit above iOS 9.3 - 9.3.3 pages to follow Jailbreak guides according to your iOS version

iOS 9.3 beta Jailbreak

Warning-  This tool was only for iOS 9.3 beta version.  Skip this process if you are iOS 9.3 - 9.3.4 public iOS user.
Enable Airplane mode, disable touch id /passcode and Find My iPhone

iOS 9.3.4 jailbreak compatibility

We have checked the iOS 9.3.4 jailbreak tool on below iPhone and iPad models. So still we did not find any error on this tool.

iPhone 6S & , iPhone 6 Plus & iPad Pro
This Jailbreak must work with following devices

iPhone 6,  5S,  5C,  5, 4S.

iPad Air & Air 2 , iPad Mini 1,2,3,  iPad 4, iPad 3, iPad 2 and iPod touch 5/6

Jailbreak iOS 9.3 without computer

You don't want to use a computer for online Semi Jailbreak process. Just visit Semi Jailbreak official website or Pangu iOS 9.3 webpage from your iPhone, iPad or iPod touch to complete the Jailbreak process. You don't need to download a Windows or Mac tool at all for this process. Read more about iOS 9.3.4 Jailbreak without a computer

iOS 9.3 - 9.3.4 & 9.3.5 Jailbreak

You must downgrade your iOS 9.3.4 version before starting the Jailbreak process. This method is only for iOS 9.3.4 users. iOS 9.3.5 users cannot use the Windows tool for Jailbreak their iOS version at this time. Don't upgrade to iOS 9.3.5 if you are iOS 9.3.4 user at this time.

Jailbreak iOS 9.3 - 9.3.3 versions (except iOS 9.3.4/9.3.5)

Why should install iOS 9.3.5?

Install if you want to increase device security

Apple brought several security updates along with 9.3.5 update. If you are not interested in jailbreak, iOS 9.3.5 upgrade is worthwhile for you.
Install if you have iOS 9.3.4 issues

If you have poor device performance after upgrade to iOS 9.3.4 like battery drain issue / App crash issue upgrade devices to iOS 9.3.5 version. iOS 9.3.5 have better device performance more than iOS 9.3.4 version.

Why Apple released iOS 9.3.5 suddenly?

At this time we are very close to iOS 10 final release. So Apple wants to fix Pangu jailbreak permanently before release iOS 10 full version. Even Luca Todesco successfully demonstrated iOS 9.3.4 jailbreak few hours after iOS 9.3.4 public release. So these are the main reasons for iOS 9.3.5 release.
Pangu Jailbreak is available for all iOS 9.3 versions. iOS 9.3.5 is the latest iOS version at this time. Apple released the iOS 9.3.4 to fix the latest Pangu untethered Jailbreak. However, The team is working to release the untethered   Jailbreak for iOS 9.3.4 and iOS 9.3.5. It will not be hard at this time. Pangu latest tool supports for iOS 9.3.4/9.3.5 partially. You can fully Jailbreak all other iOS version using Pangu tool
Tap the following button to Jailbreak for all iOS 9.3.X versions
Jailbreak iOS 9.3 - 9.3.5

Luca's Jailbreak for iOS 9.3.4 & iOS 10.0.1

Apple patched the Pangu's iOS 9.3.3 untethered jailbreak releasing iOS 9.3.4/9.3.5 However iOS 9.3.4 is also jail breakable according to Luca's experiment. We don't have any gurantee about iOS 9.3.5 fully untethered Jailbreak. Please check back soon for more information.
Popular Italian hacker Luca Tedesco has published for iOS 9.3.4 Jailbreak & iOS 10.0.1 Jailbreak related images through his Twitter account. However, Luca, The Hacker released a video to prove his Jailbreak work for iOS 9.3.3. But he has never released the Jailbreak for public.
Unfortunately, Jailbreak community cannot expect the iOS 9.3.4 Jailbreak as well as iOS 10.0.1 Jailbreak from Luca. He has never released the jailbreak, and he will not release the Jailbreak to public. Even, He didn't share results of his Jailbreak experiments/hacking with Pangu team.
Semi Jailbreak method is also compatible with iOS 10 - 10.0.3 versions. Unfortunately, There is no Jailbreak method is available for iOS 10.1 and higher iOS versions at this time.
Apple just released the iOS 10.2 for the iOS developers. There is a Jailbreak alternative method available for iOS 10.2 to install the Cydia with limited functions.
However, zJailbreak will be the best Jailbreak alternative for non-rooted iOS 10.2 devices with many more functions. Read more about the iOS 10.2 Jailbreak.
iOS 10.3.2
iOS 10.3.2
iOS 10.3.2 is the upcoming latest version for regular users.  At this time iOS 10.3.2 Beta available for iOS developers. Yalu1032 Beta IPA is also available for iOS 10.3.2 jailbreak.

iOS 11
At this time Apple is working to release the first Beta of iOS 11 version. Most probably iOS 11 First beta will release on next WWDC live event. You can download iOS 11 Beta everybody else using Sylorix as a Free and without a developer account.

Yalu 1032
At this time Yalu1032 is beta stage. Most probobly Luca Todesco would release it after iOS 10.3.2 final update. Check Yalu jailbreak page for more details.
iPhone 8

Apple planned to release new iPhone 8 device with glass body and edge to edge display. Most probobly iOS 11 would be operation system of the iPhone 8.

Cydia for latest iOS versions