This is the first stage of the two stage process which maps put all the timings. What you do is this:
Add up all the times as you go from start to finish, so if the first task has a duration of, say 4 weeks and the second one takes, say, 7 weeks, then the earliest start date of the first one is after zero weeks (so you put a zero in the top left corner of it's box) and the earliest start of the second one is after 4 weeks, so you put in a 4. On the third task you put 11 because that's the earliest you could start it, you can't do it sooner than that. It's just adding up. The largest total from the various routes is the Critical Path.
Things get interesting when you then do the backward pass, ie the same but from the finish, taking the numbers off the critical path total. So if the total came to 50 weeks and the last task was 4 weeks long you would put 44 in the bottom left corner - it must be started by then, so that's the latest start.
On the critical path the earliest and latest starts are the same, but on the floating tasks they will be different. The difference between them is how much float you have for that task - how much it can move and still not hold up the project.
The earliest and latest finish (put in the right hand corners) are the same as the starts but with the duration added. So in my example that I started with, EF is 4 for the first task, and 11 for the second. and during the backward pass the LF for the last task is 50.
All this easy if you are shown it and then try it on a real diagram rather than just in words....