Stranded to stranded seems the easiest with a wire nut. Twist tightly
with lineman's pliers, trim to length, add the wire nut. I have
colleagues who add electrical tape on the theory it can prevent
vibration from loosening the connection in the future. I don't do it,
looks sloppy to me.
Solid to solid is okay with a wire nut but very easy to mess up.
Larger sizes don't seem to twist. I make sure the wires are exactly
straight and exactly in contact for the whole stripped part. Most of
the failures I've seen were from incompletely twisting solid
conductors, and yes in one case it caused a fire.
Solid to stranded I have no faith in at all. Better to use a screw
connection I think.
If you type chocolate block connector into Google and hit Image there
are some good photos.