dial-up is where u use the phone line n connect it to ur computer for internet access. this is the slowest method and u cannot use ur phone when on the internet...
not sure bout the others
i dont think they are really connection types tho.
the basics are dialup
DSL whish is a little faster than dialup(middle of the road)
and then there is broadband cable connection which is pretty fast. prolly bout the fastest u could get.