Drilling angled holes (also called pocket holes) can be accomplished
with or without a jig. The problem with attempting to
"start" the drill bit at an angle is that it will
"walk" along the board.
The quick solution is to start the hole by drilling straight down
into the wood. After the depth of the hole is roughly equal to the
width of the bit change the angle of the drill and continue the hole.
Other methods for drilling an angled hole involve the use of
special tools or jigs. Commercial pocket hole jigs can be purchased
for under $15 (click
here) These jigs are made from metal for longer life and some
models have integrated clamps to secure the jig to the wood.
A simple pocket hole jig can be made by 1) drilling a straight hole
into a block of wood. 2) Then cut the board at the appropriate angle
and clamp it to the workpiece. You may need to notch out a section of
the jig to clamp it to the workpiece.