Start by finding a strip of wood with a thickness you're comfortable with. Each rune is approximately one inch (2.5cm) wide, so you would need about 25 or 26 inches (~70cm) of material (24 runes, 1 wyrd/blank rune, and a little allowance). I prefer to cut the strip into 2 pieces of 12 inches or so.
Clamp the strip down onto a table and draw out the runes with a pencil. Next, cut the runes with a razor, sharp knife, box cutter or Stanley knife. I have tried various other methods, including Dremel, and none have been as successful as a sharp blade.
Once you're done with all 24 runes you can saw them up into individual pieces. Use a 24T hacksaw, it leaves less splintering. Finally, sand the individual runes down to about 220 or 400 grit. If you're not familiar with the terms, just get sandpaper that feels smooth and sand them down.
I do not use any finish on my runes, no varnish or polyurethane coats. I'm also willing to bet they didn't use those stuff back in the old days 
However I *may* oil them with a fine oil. There is one oil I really like, it is sunflower-based and used for annointing Katana and Wakizashi (Samurai swords) but I don't know what it's called. Failing which, any light aromatherapy oil or even Neutrogena will do.
Points to Note
1. The grain of the wood should be horizontal.
2. Runes only have Vertical or Diagonal lines, so they wouldn't get 'buried' in the grain. My first handcarved set had a horizontal line in the Sowilo, but hey, I was 15 then so gimmie a break 
3. Be sure you know which version you want to carve before getting your knife out.
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Examples of Variations
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 Hagalaz Variation |
 Hagalaz Variation |
 Ingwaz Variation |
 Ingwaz Variation |
Which Wood to Use?
Personally I prefer to use a medium or medium-soft wood for practical purposes. But if you want your set to last a long time, or if you forsee much use, you might want to try a harder wood. Oak cuts well, and is hardy, but feel free to try exotics like Lacewood or Purpleheart. Just remember that some exotic hardwoods are unforgiving on your tools. Of course, the 'sacred' ones like Ash, Birch etc are better for esoteric purposes...yet my first set is my favorite (miscarved Sowilo, made of leftover moulding, no idea what kinda wood it is)
The Final Caveat
The MOST important point in carving runes, or ANYTHING else, is to make damn sure you don't accidentally whack one of your fingers off. Always work with SHARP tools, and secure the strip to the edge of the table well.
Inking Runes
My #1 suggestion is to use a leaf pen. It looks like two fine metal 'leaves' with a screw through it. The screw adjusts the spacing between the leaves, resulting in a thicker or thinner line. Ink is held between the leaves via surface tension, it's principle acts much the same as a quill pen.
Blood Runes
So you want to ink your runes in your own blood? Use a leaf pen. But remember this, blood coagulates so you may wind up cutting yourself a dozen times in the course of inking your runes. I know I did.