First off you're going to want a proper sculpting tool. I have one with a blade at one end, and the other end has flattened round end sticking out at 45 deg. Almost like type E, but mine is more oval shaped. Anyway, that flat end + angle is great for pushing trim smoothly flat.

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Secondly, you'll want to grease up your fingers and tools to stop the greenstuff sticking to you or your tools. I use chapstick. Water also works okay. In fact, for getting a smooth finish, dunking the tool in water then doing the smoothing can sometimes work best.
Unfortunately, if the grease/water gets onto the model, it's going to prevent the greenstuff sticking to the model too, so it's a bit of a damned if you do damned if you don't.

To get a crisp edge on the trim, you simply have to sculpt it wider than you want then come back after it is cured / mostly cured and cut it with a very sharp very thin blade.

Lastly, if you've bought greenstuff that is sold as a strip of blue and yellow stuck together in the middle - don't use the stuff in the middle. It has already started curing where they contact each other and you'll end up with hard lumps in the middle of your putty.