Painting woodwork well is 80% prep and 20% paint. Get the prep right and the finish looks after itself.
Clean and sand. Wash the trim down with sugar soap to lift grease and old polish, then rinse. Sand the whole surface with 120-grit to flatten any nibs and give the new paint something to grip — gloss-on-gloss with no key is the classic recipe for peeling. Wipe off the dust with a tack cloth.
Fill and caulk. Fill dents and nail holes with a fine filler, sand flush. Run a bead of decorator's caulk into the gap between skirting and wall — that crisp line is what makes a room look professionally done.
Prime where needed. Bare wood, fresh filler, or any knots need a primer. Use Zinsser BIN over knots and stains (it locks down resin bleed that'll otherwise ghost through your topcoat) or Zinsser Cover Stain for general bare wood. Spot-prime, you don't need to coat the lot if the existing paint is sound.
Topcoat — two thin coats. Don't load the brush. Lay the paint on, then tip off with light strokes in the direction of the grain to level the brush marks. Let it cure properly (most trim paints want a good few hours), give it a feather-light sand with 240-grit to knock back any bits, dust off, and apply the second coat.
For colour, classic warm trim whites that sit well against most walls are Farrow & Ball Pointing and Little Greene's softer whites, or go a shade off with Farrow & Ball Slipper Satin for something gentler than brilliant white. If you want trim to disappear, match it to the wall colour in an eggshell.
Finish choice: eggshell or satin is the sensible default for modern trim — easier to apply, kinder on the eye, and touch-ups blend better than full gloss. Use a good 1.5–2 inch angled synthetic brush and don't skimp on it. A cheap brush sheds and drags every time.