Typically, you would look for volume levels to decline over the time that the pattern forms. One way to think about this decline is that buyers and sellers gradually get pushed into a narrower and narrower balance of support and resistance, which effectively drives out the interest until price can break out and begin to trend once more. If volume isn't declining, this doesn't necessarily mean that there is a problem with the pattern; however, something you should be on the lookout for is a volume spike when the breakout occurs. This tends to have a beneficial effect on the overall strength of the pattern from then on.
Another effect that can be greatly beneficial to look out for when breakouts occur is a gap in the price. This shows a surge in demand for the instrument (surge in supply if it's a short trade) which adds a great deal of price confirmation for the trader. Traders may sometimes be put off by this because they feel the trade has got away from them, but in reality this is likely to be reinforcement that you have correctly determined a breakout is occurring.
Something that traders all fear when it comes to breakout pattern trades is what is known as the false breakout, or whipsaw. This occurs when price breaches the pattern, which may lead aggressive traders to move straight into the trade. Unfortunately, what happens in the case of the false breakout is that you get what seems to be a genuine signal, only to find out later that the price retreats back within the confines of the pattern, and you are left holding a trade that is not doing what you hoped it would.
The only way you can try to combat this is by applying a filter of some sort, and the most obvious method is to wait until there have been X closes outside of the pattern. If you are looking at daily charts, then you may decide to wait until the price has closed outside of the pattern for two days before entry. There are other means of avoiding this type of false breakout. Some traders choose to wait until the price has moved twice the average true range (2ATR) outside of the pattern. None of these methods will guarantee that you won't suffer false breakouts.
The previous chart demonstrated an example of an ascending triangle with an upward breakout. As there is no directional bias as to which way patterns are going to break out, we also need to look at an example of what a downward break on an ascending triangle looks like.