Outside of Kathmandu and Pokhara, the ‘squat toilet’ is the norm, except in hotels and guesthouses geared towards tourists.
Next to a squat toilet (charpi in Nepali) is a bucket and/or tap, which has a twofold function: flushing the toilet and cleaning the nether regions (with the left hand only) while still squatting over the toilet.
In tourist areas you’ll find Western toilets and probably toilet paper (depending on how classy the place is). In general, put used toilet paper in the separate bin; don’t flush it down the toilet.
Most rural places don’t supply toilet paper, so always carry an emergency stash.
More rustic toilets in rural areas may consist of a few planks precariously positioned over a pit in the ground.