Look for a bright object, say M 51, early in the evening and try to hold that impression. Take another turn one or two hours later when the object has risen and try to make out any difference. This works best with galaxies and nebulas because open clusters don't seem to have that much trouble with our atmosphere. Then there's the good old logbook. This is something that is very personal.
Some people just write down the things they saw with a little extra information here and there.
Then there are people who like to write down everything available on the objects seen through the scope. As with every hobby, you can do it the way you like as long as you write down something. I find it rather pleasant to read how things looked ten years ago. As you move further with perhaps a new and bigger telescope you can compare how things looked through the scopes. Also write down the special events which occur every now and then.