freshstart, no tumble drier here. I think there are 2 things that are key: taking stuff out of the machine as soon as it's finished spinning (all our stuff gets spun at 1200 rpm) and giving it a good shake when you get it out. When I say "shake", I mean holding the garment at the top for trousers, bottom for shirts and tops, and giving it a good flap, so it makes like a cracking sound.
Then get it on a hanger straight away. I hang stuff from the curtain rails upstairs, so that heat from the rads helps it dry, and crack the windows a bit so that the damp air escapes.
I run my thumb and forefinger along the sleeve creases of DP's work shirts, and they tend to stay in, even in cotton ones.
The "flapping" is a bit impractical for sheets and duvet covers, but I fold them in half and hang them from those hangers that have a springy clip on. Then, when it's just a teeny bit damp, it gets folded and put in the airing cupboard. All our bedding is cotton, and the only creases are where it's been folded.
In the summer, everything is line dried when weather permits. It's very windy where we live, and any creases get blown out.
Jumpers are given the "flapping" treatment and dried flat on an airer, but on top of a towel so they don't get lines from the airer.