Bigger holes are no problem, even if you don't have all the pro gear.
If it's a hollow-type hole, stuff newspapers in, then put papier-mache on the spot to hold everything in place. Plaster/spackle over it when dry. I usually put the papers in damp and gluey.
Non-hollow-type hole... you just don't need the newspapers.
With older houses (lathe and plaster/horsehair mixes, clay walls, etc.) bonding can be a problem. Make very fine papier-mache, use it as wet as possible. Add PVA to the mix.
(Most white glues are PVA.)
I love fixing holes in walls....