This is where you really have to start using pings A LOT. Gratz if you already are, but its always best to be pinging every 30 seconds to let your team know during later phases of the game if you go off to farm or push a lane. Ping that you're on the way and say "pls don't engage 4v5 I just need to push this lane quick" or "hold up for 1 min so I can clear bot".
Communication is vital and it's what most players lack.
This is where in solo que, you can't rely on your teammates to NOT engage if you don't tell them what you're doing. You must lead/communicate to succeed. Your jungle amumu is going to forget that you went bot lane right as everyone started to group. He is going to look for that opportunity to get a good bandage and engage. Then he'll look at the minimap after the fight is lost and see you weren't there. Simple pings will let him know to be more careful/patient and not go for the grab until you get there 30 seconds later.
As far as deciding when to split push or group up, you have to just practice assessment. Do you have the better team fight comp? Can you actually win a team fight if all 5 of you engage against their 5? Or will you just be stalling at the enemy inhib tower waiting for someone to make a bad decision? Is baron up and is it warded? If you go bot by yourself with no wards on baron during late game you're basically handing it to the enemy team.
You have to voice what you think the team should be doing at different phases. If you think your team is behind and can't win fights, you need to tell them to put lots of wards up, keep farming, and do your best to not engage the enemy OR you need to ward up and try to catch their team when they aren't grouped. This actually happens quite a lot, especially if the other team is ahead early in the game. People will be fed and get overconfident and go off by themselves. Take that extra killing spree gold if you catch them enough the other team might just fall apart by fighting among themselves.
It's a lot of calculations and sometimes the best you can do is guess. But practice and being aware of what you need to factor in will help you make consistently better decisions leading to victory.