There are many methods one can use to obtain sequencing quality DNA. I
myself prefer the Promega wizard miniprep kit (no affiliation) because
it's quick, cheap and easy. There are a multitude of kits on the market
for this (this is one of the few uses I can actually justify buying a
kit for.) Alternatively, you can do a PEG precipitation or a LiCl
prep. These protocols can be found in your standard cloning manuals
(e.g., Maniatis, Current Protocols, etc.).