I'll try to make this as simple as possible.
1. Go Here: Realm of the Mad God Private Servers - MPGH - MultiPlayer Game Hacking & Cheats - Hacks, Cheats, Downloads, Trainers, Games This will take you to the Private Server Section of MPGH.
2. Find the Private Server of your choice. (Pro tip. Find Threads with the word [Release] Next to them.)
3. Find out if the Private Server is on Hamachi or VPS. This can be accomplished by reading the post itself. Read Carefully. (If it says you need Hamachi, Google Log Me In Hamachi and download it. Then, if you need help afterwards, find a tutorial on how to connect to a Network via Hamachi.)
4. Download that file attached to the OP's (creator of thread) post. (If it says attachments pending approval wait a few hours or a day or however long you want to wait. Keep track of the thread. Do not beg for approval. It is frowned upon HEAVILY.)
5. Open it in Adobe Flash Player and/or any Internet Browser of your choice.
6. ?????
7. Profit.
P.S. I don't think I can make this any clearer, DO NOT BEG FOR ATTACHMENT APPROVAL IF YOU CAN'T DOWNLOAD IT. Thanks!