[AT&T] If you're confused about rooting, recovery, and custom ROMs, look here!!
After answering this question many times, I decided to compile my best efforts into one quick guide with links to some even better guides! All credit to the creators of the guides, tools, exploits, and ROMs listed below...I'm just making a tidy little post with a summary.
IF YOU READ BEYOND THIS POINT YOU WILL MOST CERTAINLY END UP VOIDING YOUR WARRANTY (and you will learn how to un-void it too!). YOU HAVE THE CHANCE OF BRICKING YOUR DEVICE AND CAUSING OTHER HORRIBLE DISASTROUS CHAOTIC EFFECTS. I AM NOT LIABLE FOR ANY OF THE KNOWLEDGE YOU GAIN HERE THAT MAY LEAD TO ANYTHING NEGATIVE! Always research, research, research, and then proceed carefully when you feel your are ready. This is not meant to scare you away, it is meant to make it CLEAR that you are taking a risk, however small!
WARNING: CLICK HERE IF YOU ARE ON AT&T FIRMWARE MF3
(to check your firmware, go to settings/more/about device/build number <--- the last 3 letters of your build number will either be MDB (oldest, original firmware), MDL (latest firmware with working loki (bootloader exploit)), or MF3 (latest update, broke loki and motochopper root exploits)
If you are on MDB or MDL, make sure you do not take the MF3 update otherwise you will never be able to downgrade and retain the current exploits! The first link below (required reading #1) will show you how to use root and Titanium Backup to freeze the updater files, preventing any OTA (you can unfreeze them if you choose). Beware, since this OTA will AUTO install.
REQUIRED READING #1:
[GUIDE][INFO] The beginner's info thread (aka. the noob helper) - xda-developers
REQUIRED READING #2
[HOW-TO] The All-In-One Root/Backup/Flash Guide - [I337 & I337M] - xda-developers
ROOT AND RECOVERY
Next I suggest you use this tool to make the process of rooting and/or installing a custom recovery very simple. The tool will root you device and then give you a choice between TWRP (Team Win Recovery Project)...which is the latest and greatest...and the tried and true CWM (ClockWorkMod recovery). I've used this tool and it worked flawlessly. You can download the "slim version" unless you need to return to stock (more on that later) (note: I do not know if this works for mac!):
[TOOL](OneClick)Updated 7-8-13 ATT ROOT RECOVERY ODIN LOKIFYED - xda-developers
On a side note, the CWM version in the above tool does something called auto-Loki. Loki is the exploit that gives us access to the bootloader in a way similar to unlocking it (since we don't yet know how to unlock it!)...some custom ROMs require that you Loki them...this version of CWM by Shabbypenguin at XDA does it for you automatically, if necessary. You can read more here:
[RECOVERY]SGH-I337 OUDHS Recovery - now with smart auto-loki - xda-developers
Now you have a recovery, how do you get there!?
It's not always as simple as it seems. I love that my ROM-of-choice (Goldeneye) has an advanced reboot menu included. When I hit reboot, it gives me the option to reboot normally, do a hot reboot, enter recovery, or enter download mode. You can get the same sort of thing with a free app like this one:
You can also do it manually, though sometimes it's a little tricky! Long press the power button and choose "power off". Give your phone a few seconds to turn off completely. Once it's off, press and hold these 3 buttons at the same time: POWER+VOLUME UP+HOME. Look at the top left of the screen - as soon as you see little blue text saying entering recovery, let go of all buttons immediately...but be ready...if your phone vibrates (it might be trying to reboot normally again), press and hold those same buttons again until you see the blue text again...then let go immediately. Now you will see your recovery!
One of the best reasons to install a custom recovery, even if you aren't going to use a custom ROM, is for the NANDROID function. This makes a backup of almost everything on your phone. I believe the only things it won't do are your baseband (aka modem) and kernel. Your data, system, cache, and bootloader are backed up. At any time, you can boot to recovery and restore from your NANDROID, returning to almost the exact same state you were at before. ALWAYS DO A NANDROID BACKUP BEFORE FLASHING ANYTHING IN RECOVERY and it's wise to keep the latest copy on your external SD card as well as a duplicate + old copies on your computer!
What is "flashing"?
Now that you have a custom recovery, you can do a lot of things like NANDROID backup/restore (see above), wipe/format partitions, wipe cache, and flash zip packages! ROMS and other mods usually come in "flashable" zip files. You put these files on your phone, then enter your recovery and "flash" them, which is another way to say install them. Boot to recovery and choose the option to flash a zip (there's another option to flash from your external SD card). Pick the correct one (carefully!) and proceed to flash it! You can then flash more stuff or reboot your phone to see what you did. I strongly suggest you make a NANDROID BACKUP before doing this, especially if you're flashing a ROM!
Now you just need to pick a ROM:
1) if you want Google Edition, is iB4STiD's Kangabean 4.2.2 Google Edition ROM:
|ROM| |★.:KANGABEAN:.★| |ATT&CAN|►GOOGLE-EDITION◄|JB|4.3 + 4.2|LOKi'D|July.26.13| - xda-developers
He has a 4.3 Google Edition version in that thread as well...you can pick which one you want...but the 4.3 is not going to be 100% perfect since it's based on a leaked firmware. In the next few weeks, we should get access to the official 4.3 Google Edition for the S4 and you can be sure he will rebuild his 4.3 ROM with those files and you'll want to upgrade then.
2) if you decide Google Edition isn't for you, he also makes two excellent Samsung Touchwiz-based ROMs: Goldeneye (this is my current ROM-of-choice, it's based on the latest international firmware which is several updates ahead of the latest AT&T firmware):
|ROM| |★.:GOLDENEYE:.★| |ATT&CAN|►XXUBMGA◄|APP2SD|JB|TW|LOKi'D|July.29.13| - xda-developers
3) and MDOB (based on the latest AT&T MF3 update with some nice modifications):
|ROM| | ★..:MDOB:.★ | |ATT&CAN|►UCUAMF3◄|APPS2SD|JB|TW|4.2.2|LOKi'D| July.30.13| - xda-developers
4) There's even a ROM out there that is almost untouched AT&T MF3...like the OTA you could take but it won't prevent you from rooting and changing ROMs like the actual OTA does:
[ROM][7/15] - AT&T Stock Rooted De-Odex "MF3" - Latest OTA! - No F/W Update Required! - xda-developers
5) The infamous CyanogenMod - this is a custom ROM based on the AOSP (Android Open Source Project) - here's a link to the official version:
[ROM][Official][4.2.2] CyanogenMod 10.1 Nightlies for the Galaxy S4 - xda-developers
6) The other famous "custom" ROM is AOKP. Many people wonder what the difference between AOSP and AOKP is...so I'll give you a link to both a good explanation and the appropriate XDA forum to get started. Let's start by saying AOKP is based on AOSP...and AOKP is the name of a ROM whereas AOSP is the name of a project where Google gives us access to the source code for Android!
[ROM] Task650 AOKP (Jellybean 4.2.2)(7.28.2013) (AT&T) - xda-developers
AOKP is a popular new ROM, what are the differences to CyanogenMod?
7) There are so many more ROMs available...remember this is just a starting point based on my favorites. Always read the instructions given by the ROM developer before flashing it! Avoid "dirty flashing" unless you're certain it's ok. Dirty flashing is when you flash a new ROM without wiping your device first...it leads to many problems and if you dirty flash and then complain about your problems, someone will (possibly rudely) tell you to go away until you do a "clean flash"!
Ok so now you want to get back to STOCK AT&T, fine then!
If you want to make life easy, go back up to the link above to the TOOL I suggested for rooting and installing recovery. Download the full version, which includes the ability to "Odin back to stock". It will use Odin to put the stock AT&T MDL firmware back on your device. This will remove custom recovery and any ROM you currently have...and then you can do it all again! If you want to get rid of root as well, just do a factory wipe/reset in your chosen recovery before using the tool to go back to stock. If you want to read more about the process, have a look at the manual method for the "Odin back to stock" procedure:
[FACTORY STOCK] GS4 Stock Firmware Odin Package- Original Factory ROM - xda-developers
<--- video guide to help you with ODIN
Firmwares | SamMobile <--- firmware download link. Search for "i337" and the first result should be I337UCUAMDL which is the latest AT&T firmware PRIOR to MF3.
Make sure that after you complete this process, you take measures to avoid the MF3 OTA update which will be eager to get on your phone once you're back to stock!
Custom Kernels, flashing modems, modifications etc.
Woah there buddy. Master all the above and then research more if you really want to go deeper into this craziness!
I hope this helped!