If you teach English conversation in a small, informal classroom (maybe one to five students), most of your job is probably just making conversation, trying to get the students to speak English! And if that's true, you really can't afford to ignore their mistakes. If they don't get the idea that something like "Yesterday, I was go to work," isn't quite right, they'll probably never fix it. Or at least, it'll take a really long time.
So you've got to do something. But don't worry; you don't have to be a jerk about it. The way I see it, you have four options:
1) Play dumb. Even if you were able to understand your student perfectly fine, you might want to pretend you missed something. This can include interpreting the student's sentence literally if the error produces a change in meaning (as in "I really like dog!"). Or it might just be something like "I'm sorry, what?" or "What did you do?". This gives students a chance to correct themselves, but interrupts the flow of conversation a little. If you use this method, the student has to be able to self-correct without any help.
2) Prompt them. If there's no possibility of misunderstanding the student, but you just want them to notice (and fix) the error, you can try repeating there sentence up to the point where it went wrong: "Yesterday, I..." This makes it fairly clear that the student needs to correct a mistake, but it can sound a little condescending and definitely interrupts the flow of conversation. If you do this sort of thing, try to make it clear that there's no huge problem, just a little something that could be better. You want them to talk freely without being scared of messing up!
3) Fix it. Just repeat their sentence back, correcting the error yourself. You can even disguise it as a question: "You went to work? What time?". This is a very natural, easy way of correcting speech errors, but it's not always possible. For instance, if the student says, "I going to school," you can't very well say, "You are going to school." That's just confusing. Another weakness is that the student might not notice there's any problem. You're only giving positive reinforcement, which may be too subtle.
4) Note it. If you don't want to discourage the student or interrupt the flow of conversation, you might not want to correct the student's error right away. If this is the case, you should really make a note of their mistake, especially if it happens again and again. Later, you can do some sort of exercise that focuses on the problem you noticed in the student's natural speech.
All these methods can also be applied to helping children acquire their first language. Most kids supposedly don't need any help, but some kids do, and anyway it couldn't hurt.