I am aware there is already a guide for downloading ATLauncher and Pixelmoncraft, However it hasn't been updated since 2014, and now many of the websites and the launcher look very different. Following the many requests for help installing in the discord server over the past few days I have decided to make a more up to date post.
First go to http://www.atlauncher.com/downloads and download the ATLauncher for your operating system.
Once this is done place the downloaded file in a folder, this stops it from creating many subfolders in your downloads folder or desktop
Once it has started up for the first time it will request your Minecraft username and password. Enter these and click 'switch to account now' when it pops up.
Scroll down the Packs menu until you see Pixelmoncraft listed click 'New instance' and select any of the optional mods that are available if you wish to do so.
After a short while it will open a browser window to the Pixelmonmod page http://mirror.pixelmonmod.com/core/5.0.4/ Download this file, if it asks you if you want to keep the file or delete it, click 'keep' and then place it in the folder that the ATLauncher specifies if it did not automatically go there. Then click 'I've downloaded this file' so it can finish the install.
Then next step is to check whether you have 64 bit Java installed on your system [YOU WILL NOT BE ABLE TO LOG ON SUCCESSFULLY WITHOUT THIS]. Go to setting then Java/Minecraft and check how much ram you can allocate, if you only have 32 bit Java then the maximum you can allocate will be able to allocate will be 1024Mb and you need at least 2560mb to play properly. In order to install 64 bit java go to http://www.oracle.com/technetwork/java/javase/downloads/jre8-downloads-2133155.html and select the 64bit download for your operation system. It will then run the Java installer which will guide you though the process of installation.
Once you have done this you are ready to come play!