Another poster has already mentioned that this is
an easy job for a drill press, and that's certainly
what I'd do. But that's because I own a drill
press, and there is some possibility that you don't, or
you'd be using it instead of asking the wreck for help.

So if you don't have a drill press, make a 45-degree
drilling jig by drilling a hole of the desired
diameter in a block of reasonably stable dense scrapwood
(cherry is ideal, but anything in the scrap box will work,
except maybe balsa) 2" wide (the width of your workpiece)
and 1.5 or 2 inches thick. For this job you _can_ use the
trick of drilling a perpendicular hole and then slicing the
jig at a 45-degree angle.

Once you have your drilling jig, glue a small piece of wood
to one side to give you a fence to register it against the
side of the workpiece, clamp it in place on the workpiece,
and use the hole to guide your drill bit.

You'll still have the problem of spacing the holes evenly,
but that's just a matter of careful layout. You can
also use a spacer block: clamp the block to the workpiece
next to the jig, unclamp the jig, move it to the other
side of the spacer block, clamp and drill the next hole,
and advance the spacer block and the jig leapfrog down the
workpiece.

If you're planning to drill many holes (say, hundreds)
you might want to consider a metal sleeve for the hole
in the drilling jig, but a wooden jig will hold up just
fine of smaller numbers of holes.

Another poster has suggested that you might want to consider
cutting the workpiece to length _after_ you've drilled the
holes. That is excellent advice - makes the whole
process much more forgiving.

Larry Spitz wrote:

I would appreciate some net-advice on how to drill a straight line of holes
at constant spacing and at a 45 degree angle to the surface of the wood.
Since I want to do this on the 2 inch surface of a 1x2x24, it is not
practical to drill perpendicular holes and them to slice the workpiece at 45
degrees.

The angle and the spacing must be held as constant as possible.

It is the same concept that is used in Cado modular furniture,

Let me try an ASCII drawing

__________________________________________________ __________________
\\ \\ \\ \\ \\ \\ \\
\\ \\ \\ \\ \\ \\ \\ 1"
__________________________________________________ __________________
24"

Any tips would be appreciated.

Larry