My boots are leather so here goes with what I do to clean my boots on walks and to store at home.
Firstly for at home I will always leave my boots to dry off usually overnight - just on some newspaper away from any radiators or the fire, slow drying as they are leather. It's easier to remove dry dirt than wet. Once dry I'll bang my boots together to remove the worst of the mud, if I'm off out again there is no point doing more than this.
If not, I'll then use a soft bristled brush to get as much mud off the leather and soles as possible. Next I'll wipe them over with a slightly damp cloth or kitchen roll, this leaves the leather clean enough so that I can reapply a protective coating - something like NikWax for leather. They then live in a hiking boot bag.
On route and out camping, well this depends. I have two tents, one is larger with living area separate to sleeping so I don't really mind leaving my boots in there, the other is much smaller with only a little area outside for bags and boots. I aim to never step inside the actual tent with my muddy boots (this helps keep as much mud from getting in the tent as possible) but to clean them I will do little more than find some damp long grass (dry works but damp is better) and drag my boots through them. We do this a lot when out walking in the British countryside as you will get a lot of farmland and it's better than leaving mud on a fence post. Also I will stomp a little in standing water - a puddle on the roadside for example, again this only helps if you have one, but helps get rid of the mud on the sole of your boot.
If you're lucky with the weather on hikes and camping you should be able to dry your boots over night and bang them together in the morning to remove as much mud as possible. If you have the space for a microfibre cloth you could probably give them a good wipe over if you want to - but if you're going to get muddy again the next day then I'd say don't bother, just clear as much mud off the sole of the boot (a knife works as well, not a sharp one, or a stick to clear your sole out) so that you can stand evenly without discomfort.
The best and easiest way I've ever cleaned my boots is to go for a walk in the snow, they come back sparkling. I'll leave them to dry, apply NikWax and they're good as new. It's just a shame the south of England only gets snow once every few years.