I like buying breakouts on rising and falling wedges and where it seems obvious a stock is done moving in a certain direction - like a really clear elliott wave setup. I also look for divergence with indicators and good recent price movement. I use the Macd, Stochrsi, rsi, dmi and moving averages on the price. I'm suspicious of breakouts where my indicators are overbought. I'm also suspicious of a breakout up on a rising wedge - generally you look for a breakout down with a rising wedge.
Basically, with a breakout, I want a bullish or bearish chart pattern with my candles, divergence with my indicators and indicators that aren't played out.
I've also found that failed breakouts are often good trading opportunities.
Be careful listening to me. I'm just an amateur.