I'm far from expert in artifact hunting but I do the majority of my hunting in creeks and very little in fields. A lot of this is obvious but make sure to look in the water, on gravel bars, and in the sides of any cut banks. Gravel bars are especially good places to look especailly at bends in the creek. Check after each big rain because new stuff will be exposed. Go slow. You will notice that rocks and debris will tend to be naturally sorted by size....I spend a lot of time focusing on areas where there is a lot of gravel that is palm sized and smaller. When I come to an area full of fist sized or larger rocks I turn my attention toward looking for axes, nutting stones, hammer stones, etc. Go slow. As far as spotting points goes it's the same as in field hunting only you have a lot more to look at. Go slow. On big gravel bars I do a grid search moving slowly back and forth checking and re-checking where field of view overlaps. Also I generally start out on the downstream end of the creek and work upstream so that any mud I stir up doesn't cloud the water ahead of me. If I know I am in an area that produces artifacts I will spend 4-6 hours and probably cover less than half a mile of creek bed. If I have say 6 hours to spend I'll go upstream for 4 hours, then turn around and use the remaining 2 hours retracing my steps...it's amazing what a change in perspective can do toward allowing you to find stuff you missed the first pass. Be sure to check any seconday creeks that feed the creek you are focusing on. These may be nothing more than runoff ditches that are dry most of the time or they may be streams that are always running.
The farm I do most of my hunting on has 5 small creeks that all dump into one larger creek. The larger creek runs year round, the smaller creeks run most of the year, but almost dry up in the summer unless it rains. Off of each of the 5 small creeks are runoff drainages between ridges or coming off fields and pastures. I look anywhere that I see exposed rock...especially if some of that rock is flinty. I've found most of my points etc in the smaller creeks...possibly because there is less to look at in them and the artifacts stand out. The bigger creek most likely has many more artifacts in it but the water is deeper, there are huge sandbars and gravel bars that hide artifacts very well, and there is more leaf debris piled up on the gravel bars. Mostly though you just have to take your time, use a long walking stick to turn over interesting pieces, and don't neglect anything that looks like it might have been worked. Go slow....good luck. I'm sure others will have more to add.
