The real best way to paint baseboards in a room with carpet is to do it BEFORE the carpet goes in. But if like me, you are a mild idiot at times, and need to do it AFTER your lovely new carpet has been installed, or even if you are painting in a room that already has carpet i'm here to say i tried a variety of techniques and this one is the winner.
First the different techniques i tried
Technique A - tape the carpet - this didn't work too well for me.
My carpet is brand new and quite fluffy, so the tape did not stick down well. It would pull up and roll away from the edge so i never got a reliable barrier between the paint and the carpet.
Technique B - use a putty knife to shove newspaper or a thin drop cloth under the edge. This also did not work for me, except for one 2' long section, my base boards extend about .5" below the top of the carpet so i really couldn't wedge anything under there, and even in the spot that i did - it was not too easy, or clean to get it back out.
Technique C - pull the carpet away from the edge with a putty knife. I found this video online, and it was a bit helpful. HOWEVER my attempts to pull away carpeting as described just ended up fluffing the carpet further, getting fibers all over the place and making the edge actually higher.
The winner - Technique D - the best technique i found was just to be slow and careful while mushing the brush up and down along the bottom edge. it ended up being the cleanest and quickest with the least amount of bleed through and the most through coating.
step 1: accept that you WILL get some paint on the carpet fibers - but know that it will be minimal and barely noticeable when your face isn't 5 inches from the edge- like it will be as you do steps 2-7.
step 2: I would dip the tip of my brush in my cup of trim paint and wipe it down on one side - like so
step 3: then, with the paint-heavy side of the brush against the trim, i would push my brush hard in to the trim to fan out the bristles of the brush.
step 4: then slowly push the fanned out brush down along the bottom edge, sneaking it between the tops of the carpet and the baseboard.
Step 5: once down deep enough i would give the brush a slight wiggle to deposit paint along the bottom edge.
step 6; then pull straight up along the base board.
this technique was surprisingly quick and effective.
step 7: I would just paint the rest of the board as normal - and having the top edge of the trim tapped off on the wall really helped to make it all go faster.
then - because you;d done such a good and thorough job for the bottom edges on the first coat - for the second coat i just quickly painted along the middle 4/5's t\of the baseboard, avoiding the carpet edge entirely and now the trim looks great - especially from a little distance ;)
i can't say i would ever want to do this again, as it is quite back breaking work, hunched over and moving slowly around the room. But it's nice to know i found a method that can work in pinch.