'to go on doing something' means to continue doing something.
- He didn't even look at me. He just went on working.
- I can't go on working so hard. I'm going to make myself ill.
'to go on to do something' means to move on to something after you have finished.
- First he told us about the present situation, then he went on to tell us about the future.
- If you have no further questions, I'd like to go on to the next part of my talk.
'to go on' means to happen.
- What's going on outside? There's a lot of noise.
- There's not much going on this afternoon. It's very quiet.
'to go out' means to leave home to go to the cinema or the pub for example.
- I won't be home tonight. I'm going out with Kelly.
- We're going out for a beer tonight. Would you like to come?
'to go over' means to review something to check it.
- I'm not sure my figures are accurate. Can we go over them again?
- He went over the main points again to be sure we had understood.
'to go through' means to experience an unpleasant or difficult time.
- It was terrible. I don't want to go through that again.
- He's going through a very difficult time what with his divorce etc.
'to go through' also means to examine something carefully.
- The customs officer went through their bags looking for drugs.
- I've been through his papers but I can't find the one I'm looking for.
'to go under' means to fail or go bankrupt.
- Three thousand companies have gone under so far this year.
- Cash flow is the reason that most companies go under.
'to go up' means to increase or rise.
- The number of jobless went up 0.5 percent last month.
- It's very expensive now. The price has gone up by ten percent since January.
'to go with' means to support an idea or the people proposing a plan.
- I think Jack's right. I have to go with him.
- We should go with Sue's idea. It's the best idea yet.