Look at some painting videos from Hometime or similar TV shows - or get the Black and Decker or Creative Homeowner book (about $10) on Painting.
Generally - minimize drips and splatter by only wetting the tip inch of the brush - don't let it get into the base of the bristles or up in the metal part, which also means avoid holding the brush upside down if you don't have to (though on ceilings yuou can't help it). Also, when you load the brush I wipe one side off on the tray or can so there is only "loose" paint on one side, which is the side that goes against the wall making a quick V with the bulk of the paint beforeit starts to drip, then brush that "globbed-on" (thought I would throw a technical painting term in there) V out into a painted square - others do two swipes with a few inch gap in between in the general painting direction and then brush to spread that out and fill it in. I prefer that because sometimes the V shows through with certain paints or very absorbent surfaces.
The much higher priced natural bristle brushes generally "hold" the paint better too, limiting drips. Generally, the cheaper the brush the pooer the coverage and the more issues you have - though of course buying $10 horsehair brushes means you generally have to clean and reuse them rather than throw away when done.
Splatter from roller - load the roller in the tray, then roll it down the ramp to remove the globby paint - should not "drip" as you remove it from the tray. Also - load the roller by rolling it into the edge of the paint or only across the top of the paint pool - do not "immerse" the roller. I drag it across the top of the pool (just the nappe of the roller, not the whole diameter to the handle axle) and continue up the ramp pulling a small "wave" of paint which the roller picks up as it rolls - then back down the ramp to get even coverage and eliminate the excess paint. Go relatviely slow with the roller to minimize splatter. Rolling horizontally rather than vertically also helps me limit splatter - especially on the ceiling when doing the top of walls.
