I am starting to climb my way out of lower elo (I know this because I see way more people with revive and que times have gotten longer. Either I've moved up or they moved down.) Anyway I always use revive after the windmill fight if I lose or someone starts to cap our mid or bot but I sometimes forget that I have my revive up. I mean it's just sitting there idle. Are there any other times when it is appropriate to use revive or should I continue to play the way I've been playing?

Revive is one of the trickiest summoners to use properly IMO.

I'm trying to think of an answer that doesn't boil down to "When you need it".

Here's when I use it:

1. Windmill fight, assuming your team has revive and is willing to use it. No point in getting wiped out and being the only revive to run in to a 1v4.

2. If you're in a down to the wire match and they're going to cap that bot or mid point if you don't interfere.

Those are the more obvious scenarios.

In mid game it's sort of a, "Would doing this actually help us keep a point?".

I profess that I'm no expert but these are the simple rules I use.

maybe this is just my opinion but I actually dont like revive that much in Dominion and here is why:

If I have the summoner spells to support combat (say flash/exhaust) they will matter more in the initial Windmill engagement. Assume its 4 revives vs 4 with combat summoners. those 4 combat summoners if used properly at the least will result in a 2 for 4 trade (obv dependent on champions but its not often you will see 4 combat summoners lose if a champ isnt using an available spell)

If i run a flash/exhaust flash/ignite combo I'll know that I have a certain edge over opponents using revive ghost (the usual combo) which will allow me to capture a point. (Ghost is typically used in the initial rush and thus will be down for combat).

Assuming my side wins combat you need to quickly cap the point and immediately B to make use of the gold advantage you just aquired and itemize because you know the 4 you just killed have revived and are rushing back. they'll retake the point but then its just a matter of sitting back and pushing the lane to neutralize it and then reentering combat which you probably will win because now you have the items to do it. then once you retake, go b again and just itemize again. rinse repeat.

This is of course, just my opinion.

Basically whenever it's up and when I can synchronize it with the respawns of my allies, or if I need to rush back to defend a point.

Usually after getting 4 man ganked and typing "rude".

Revive isn't like Flash on SR. You're not supposed to take it on every champ regardless of how you're going to build them or team comp; that's just stupidity; that's what you see at the very low Elo brackets of Dom because players there simply have no concept of strategy.

Revive is good on champs who will have a large influence on holding points. Whether it's a Malphite who can hold off 4 enemies for a good 15secs on his own or if it's a Nid or Shaco who can realistically interrupt 2 enemies attempting to channel a point as often as is necessary. However, Revive is highly overrated.

Garrison very often provides the necessary power swing required to make a game changing play more than a well placed Revive. The combination of interrupting all channeling enemies and "healing" the point at the same time is extremely underrated, especially when used with the mastery bonus.

But, if you do ever get the highest echelon of play in Dom, you will find that 10 Revive per game becomes necessary entirely due to a flaw in the wave respawn system; it's a flaw which can take a team that is well ahead of the other and cause them to lose with relatively little effort from the other team. This is better explained here.

To actually answer your question, you use Revive when it will matter. There's no set of rules that will dictate this 100% of the time, it's completely based on your own decision making prowess. It requires time and practice to know when to pop Revive.