Five questions to ask before engaging

1.  What advantage do we stand to gain from this engage succeeding?

There are a couple types of advantages.  Gold and experience gain/denial are the most common ones that are considered.  But you also need to consider map control and objective control in the short term and the long term.  Short-term would be "Do we dive them now to get this tower?" and long-term could be something like "Dragon spawns in 90 seconds.  If we cause them to burn all of their summoners now but don't burn any of ours, we'll have an advantage in the dragon fight."  If you push them out of a bush that they had pink warded so that you can pink over theirs, you gain map control.  All of these can be sufficient reason to force an engage.

2.  What are the chances of success?

Diving the 10 hp support with no cooldowns when you're at full hp is relatively risk-free.  Diving the 100 hp support with all his cooldowns when you're at 25% hp is usually pretty risky.

3.  What advantage do we stand to lose from this engage failing?

When you're engaging, you're almost always denying yourself some sort of resource.  Lee Sin could be taking double golems instead of ganking botlane.  Miss Fortune could be farming the creeps at tower instead of fighting in the gank.  If the engage is successful, it's probably worth it.  But if  the engage fails, remember that in addition to giving up whatever kills/gold/experience you might give up to the enemy team by failing, you're also giving up the resources that you could have been collecting had you decided not to fight.  This is especially important to consider when you out-scale the enemy into late game.  Doing nothing, you're gaining strength faster than they are because they don't scale as well with resources.  Consider also any vulnerable objectives that the enemy might be able to take as a result of your failed engage.

4.  What are the chances of failure?

Consider the chances of different levels of failure:  Failure to kill the Janna you're chasing is one thing, but having the Vayne turn the fight around and get a double kill when you try to dive her is another.  Maybe it's unlikely that it fails, but if it fails it will fail spectacularly.  Or maybe it's likely that nothing happens as a result, and there's a very tiny chance that it goes extremely poorly.

5.  Is the engage worth it?

Consider the other four questions and their answers and then use that information to answer this one.  If it's worth it, go for the engage!  If not, maybe you should wait for a better opportunity.