In order to smooth the concrete, it is physically ground. The size of the grinder depends on the amount of material to be removed. It can be anything from a regular 4 1/2" angle grinder with a masonry wheel up to a walk-behind planer with a few steps in between. The planer will remove up to 1/8" per pass. This machine would be the last resort. Things can get real ugly real fast if you don't know what you're doing. If you just have little ridges from where the edge of the trowel ran over the floor, I would start in a corner with the angle grinder and a masonry/concrete wheel to see how effective you can be and go from there.
As to the cost, I have no idea. The only project I worked on where we had to grind a slab, the work was done by the contractor that placed the slab because it was way out of tolerance for the finish flooring that was going on top of it. My guess is that it can get very expensive depending on how bad the slab is to start with. Talk to your friend. He might have contacts that could do the work cheaper than you can rent the equipment for. If not, they would at least be able to point you in the right direction. It's worth a shot.
The most important thing to think about is the dust. No matter how you grind concrete, it will create a very thick, choking, fine dust that covers anything in it's path. Wear a face mask, goggles, etc. I would also keep the surface damp to try to knock some of the dust down. I have a picture on my computer at work from the same project I mentioned in my first post where a slab was being ground. It doesn't even begin to show what that is really like. I'll try to remember to post it tomorrow. I've heard stories of the fire department being called to sites where concrete was being ground because the dust looked like smoke.
I would consider warning the neighbors (if you have any) that you'll be grinding concrete and that there will be dust. Pissed off neighbors and a possible visit from police will only add to your current frustration.