I realise there are several different things I do while climbing, I've been taking note of them this week. Here's the general approach.
On longish climbs when I want to remain seated I do this. Before climbing I change down to a low gear. I find it's better to go too low and have to change up, this technique is about feeling better when climbing and changing down on the climb might feel like defeat. I allow the bike to slow quite a bit then pick up pedalling at an easy pace and once I've found a rhythm I shake myself down and get comfortable on the saddle, holding the bars lightly, trying to relax as much as possible.
Then I focus on trying to make the effort as easy as possible- this is hard to describe but easier to do. I'm not sure what I do- possibly making small adjustments to my pedalling and breathing, trying for -what feels like- greater efficiency. I've no idea if my climbing is more efficient, but it feels better and gives me something to focus on. Perhaps if I had a power meter..
Anyway, I start off like that. Once I get a bit further up I might increase the pace, change up even. Having something left towards the top feels good. If riding with a group I might let them get away at the bottom of the hill, chances are I can catch up later.
This doesn't always work as some hills are just bastards. Without low gears there's no chance of settling into a rhythm or getting comfortable. Even with low gears there might be no chance either.