Self-Searching is basically just clicking the "Play" button on the game page and just going around the three islands search. Devil Fruits spawn every 15 minutes under a random tree on any island and despawns 2 minutes later. Keep this in mind when searching.(Notice: This method might be difficult to do, but it is simple if there are no "RKers" in the game).
Get a team of 2 of your friends and tell them to search on one island each. One person on Buggy's, one person on Shells Town or however you wish to set up your team. If someone finds a devil fruit, but it is not the devil fruit you wanted, you can trade devil fruits when you finished your search. If you got the devil fruit you wanted, well, you know what to do.
VIP Server Method
If you are someone who is rich and has tons of R$, buy a VIP server for R$300 a month a start searching around the server. This means you will be free of RKers and people who you might find to be annoying.
NOTICE: IF YOU EAT A DEVIL FRUIT, YOU WILL NOT BE ABLE TO SWIM AND YOUR STAMINA WILL DECREASE DRAMATICALLY IF ENTERING THE OCEAN. It is also noted that eating a devil fruit will give you its powers, but if you eat a second devil fruit while still having the original fruit you ate, you will reset and the devil fruit you just ate will go to waste. You will still have the first fruit powers. To eat a second devil fruit, you MUST create a new game.