Here is a walk-through by which you can successfully jailbreak your iPhone. The process is pretty simple and it takes just around 2o minutes, depending on your OS. You are going to need a software called "evasi0n".
evasi0n 7 compatibility
The evasi0n 188.8.131.52 jailbreak is compatible with all Apple touch models running the iOS 7.0 and any other device that is capable of running iOS 7.
Back up your Phone
As always, do make sure that you backed up your iPhone or iPad before attempting to jailbreak, in case your noob out.
Jailbreaking iOS 7
1. Back up your Device. Always do this before attempting to jailbreak.
2. Plug your Device into your computer.
3. Launch evasi0n, If you are on a Mac you may have to right click the evasi0n jailbreak tool, then click Open to confirm that you'd like to open it.
4. Click Jailbreak and then wait.
After a few seconds, you'll see a message asking you to unlock your Device. Tap on the evasi0n7 icon.
5. You may be asked to unlock your device one more time if you have a security code.
6. evasi0n should now give you a message saying that the device was successfully jailbroken and the process is completed.
Just click Exit.
7. Your device may reboot a few times for completing the process and that's it! You should now have Cydia on your iPhone once more.
Once the process is completed, you'll want to pop into Cydia in order to update it. The file system will be updated, but you might have to install other updates on your own. Apart from that, you're good to go.