The difficult thing is to get the new strings into the hole at the bottom. Having the Stagg in a fixed position and using a torch to see the holes and a straight top of the string helps.
Anything else is not different from a DB … except … the short pegs.
If the string is too long to be able to wind it completely onto the peg you can cut them n the silk part AFTER you secured the windings with a drop of glue, but then the stain is harder to sell or stick more of the string out of the peg hole or slot so less strings needs to be wound onto the peg.
Stay away from the headstock sides and wind (at least) once over a previous peg winding to avoid slipping. I typically wind first away from the nut slot as much as possible and the back towards the nut to fix.
If you change to a different string diameter you need to widen the nut grooves and if the grooves are deep carefully file the nut down until the grooves are less deep than half the string diameter.
Warning! I didn’t do that with my first Stagg and the nut broke at the groove. Needed to make a new one.
A larger diameter E-string can jump out of the bridge groove. The Stagg bridge is a bad design (functionally).