Work Backwards
One of the easiest ways to develop a strategy for the triangle logic puzzle is to work backwards. Start with only one peg on the board and work out where pegs would have to be to reach the one peg situation, gradually placing pegs in the holes until you have a full board. Note down each move and try a few different scenarios. This way it's possible to get a feel for the kind of moves required and the kind of positions to aim for when playing the game.
Crunch Numbers
For anyone with basic coding skills, it is fairly simple to create a number-crunching program that can work through the various permutations and tell you how many possible solutions there are for each hole on the board. Simply assign a number to each hole and create a simple calculator using a coding program. Alternatively assign zero to the 15th hole and assign one to all the 14 holes that have pegs, to create a simple binary system.
Practice
Play lots of games with the triangle logic puzzle and record every move made in every game. This allows the player to review games and also ensures full concentration on each move, making mistakes less likely. Also, by playing a lot of games, players can develop familiarity with a variety of different scenarios and tactics.
Cheat Sheets
Cheat sheets are all over the Internet and present an easy, if unsatisfying, way to beat the triangle logic puzzle. These are ready-made games for the player to follow, move by move, to ensure a successful solution. While this may not be so interesting or challenging, following a cheat sheet is a simple way to become familiar with the most effective strategies before trying to solve the puzzle without help.