What Shannon said
I go 2 to 3 months usually, sometimes a bit longer, and then change about half the substrate - our hammy uses a litter tray and I empty that every 2 to 3 days. It isn't too stressful for them when you do a substrate change - especially if you mix some of the old in that smells familiar, or sprinkle it on top. I find as they get older, it even meets with approval! It's doing it a lot and cleaning everything that stresses them. So best thing is not to clean everything at the same time. So when you do a substrate change, don't clean everything else. You can do the wheel a different week and the toys a different week again.
I also leave the nest alone if it isn't pee'd in. The hoard under the nest gradually builds up. I leave the hoard until I do a substrate change (if it's not pee'd in) as our hammy only hoards dry food - so you need to keep an eye on their habits - if you think they have hoarded fresh food that can go off, then you may need to spot clean the hoard a bit.
When I do the substrate change I tend to "prune" the bottom half/two thirds of the hoard as it gets really large and takes over the bottom half of the cage! If you do need to remove the hoard if it's pee'd in then put new food back in exactly the same place to replace it and try and leave a tiny bit of old hoard that's clean and smells familiar.
Same with the nest - if it gets pee'd in and has to be removed then try and leave a little bit of the old nest behind that isn't wet and smells familiar. Then put a big pile of new nesting paper out and they take some to rebuild the nest. Torn up strips of plain white toilet paper are best for nesting material. I keep some out in the cage al l the time (they like to forage for it) because they regularly add new bits to the nest or chuck old bits out (which you can remove when spot cleaning).
Actually I think they get more stressy about their nests and hoards than a substrate change. Main thing is keep things smelling familiar and not removing all their familiar scent.
The other thing is, when cleaning the base of the cage when doing a substrate clean - not to use anything scented as it's overpowering for hamsters and that can stress them. Unless there has been illness or disease you don't need antiseptic cleaners - just warm water is fine, or warm water with a bit of fairy liquid in and rinse well.
If you ever do need to use pet disinfectant - Beaphar and Johnsons don't smell too much - they say they don't need rinsing, but rinse it well anyway to get rid of any scent quicker.