That depends, really. I'll separate my answer into sections.
Mid game - Late game
You should always help each other. The only reasons you shouldn't help are :
You are low on health and (the enemy has ways to dive to you OR you don't have long range abilities)
If you can't fight without putting yourself at risk, don't
bother. 1 for 1 trades are generally not worth it in solo queue
unless you're a support trading for an enemy ADC or Mid.
Case examples :
- If you're Nidalee and have mana, you can stay back, heal teammates, spear your enemies, but avoid going in in cougar form unless you're sure you'll eliminate the enemy with your cougar Q and avoid damage afterwards.
- If you're Ahri, you're generally a close up assassin, which is not good when you're low health. You can throw your Q and E if they're on cooldown while running away, but don't bother with your short range W.
You know your team will lose the clash even if you help
In this case, communication is the key factor. If you truly think you can't win and you have to wait for another one of your allies before you engage, tell your teammates.
The only ones probably worth expanding on are the Jungler and Mid roles. ADC and supports generally keep bot until they need to rotate when they push the tower.
This really depends on what kind of jungler you are. Some junglers are red-buff dependent when ganking, so you have to consider your buffs as well. Generally, if your champion doesn't have a natural CC, red buff is crucial for the slow.
I wouldn't put a "how to gank" or "when to gank" part here. There are a lot of detailed YouTube tutorials for that.
To answer generally, you should gank when the opportunity presents itself. Ganking boosts yourself AND your allies, and early game is when you want your allies to have that advantage.
Damaging the enemy laner with a gank or burning their flash is a SUCCESSFUL gank. A gank doesn't need to produce a kill to be successful. If you give your laner the chance to farm freely because you made the enemy recall, that's a win.
I recommend this VERY DETAILED YouTube tutorial by ScrapComputer for Mid laning. It gives you a lot of insight on when to FARM, KILL, or ROAM.
HELP when you can. By winning a clash, even if a support gets the kill, you can take advantage of that and get an objective, and further snowball your whole team.
If there'a jungler v jungler fight happening at near baron at early game, as a Top laner or Mid laner, go ahead and help your jungler especially when your lane is pushed or you have an advantage at lane (meaning, when you leave your lane, you aren't leaving your enemy laner to get a free push or get a big advantage for you)
Don't care about being called a KSer. You are playing to win. Not playing to deny your allies of their "rightfully owned" kills. By securing the kill, you are driving your team to victory.
Protip : Mute toxic players. Press Tab and click the chat bubble button. They do more harm than good. You should still communicate via pings though. :)