I decided to write my own answer on top of Zamual due to the fact that his answer deals with what the benefits of using Promote rather than the actual question being asked: "When do you optimally use Promote?"
First and foremost, Promote should not be used whenever it is on cooldown. This will most likely lead to you pushing your lane way too much and getting ganked. Or at the very least prevent your jungler from ganking your lane.
It SHOULD however be used when:
- You are low mana/health and need to recall to heal and buy items. The Super minion can last quite a while. (Once just for fun I tried to 1v1 a promote minion as a lvl 5 Sona and almost died to it. haha) This will buy you enough time to get your items and come back before they take too many hits on your turret.
- If you are in a 1v2 lane or if you are against a really good pushing Champion (Malzahar, Morgana, Cass), use it to counter push so your turrets dont eat all your minion farm.
- Or if your 1v2 and your enemy decide to not push at all and just zone you out of any gold or exp at all. In this case the promote minion can go ahead and get the kills so you will be able to get the exp and gold from the promoted minion's kills.
- If you are 1v1ing(because you are forced into it or because you set it up) promoting a minion will deal a surprising amount of extra damage to your enemy would will not really be expecting it.
- If you have already taken down their first turret a lot earlier than you were expecting, you don't really want to push to the middle turret because that is a sure way to insure you get ganked. Just promote the canon minion so it can push to the next turret and then you can go do something else. With the new jungle spawn time, you can easily take the wolves and wraiths without messing up the jungler. Or you can try to gank another lane. Just remember to not stay in another champions lane. This will lower the exp the other champion will get and is counterproductive. Just gank and then leave.
- Use it when you are pushing as a team, it will tank the turret and your team can easily take down the turret before the promoted minion dies.
- In late game when everyone is moving together as a group, sometimes people forget that the minion still exist and can still push. Just promote one of your canon minions and watch as he BD a turret while you are teamfighting the enemy team.
This is all assuming you are not playing Dominion. If you are on dominion, you SHOULD be using promote on recharge. Mostly because there is no downside to pushing really hard at all AND the fact that the games usually last a lot shorter so you want to get as much use out of it as possible. For the most part usually the person pushing bot will optimize this the most.
Generally champions with high mobility or assassins should not touch promote. Promote are for defensive and slow champions. Champions like Heimerdinger can use this better because they usually stay in lane and set up a "base" with his turret and the super minion. Champions who are perhaps able to heal or buff the promoted minion can also get the most out of it. I think Janna would be a good choice. Since as a support she has passive movement buff AND her tornadoes are great to escape with, she can replace flash with promote. On top of that, her shield can add additional damage on to the promoted minion.