Wobbly John said:
My next door neighbour used to have a bike shop and is Mavic certified, he reckoned he could lace a wheel in 15 minutes while reading the paper - I've had one wheel built by him - never again.
Lacing the wheel is no problem, its the bits after.
It's not hard, but you do need to know what you are doing. I built my first wheel using a frame as a wheel jig, old rigida rim onto an old SA hub, copying an identical wheel.
I got it "about right" and that gave me the confidence to build wheels again. I did get better and ended up working for a while as a wheelbuilder knocking up some expensive wheels, the one I remember most was a set of seriously sturdy wheels with top-notch rims, hubs and spokes for a tour of Afghanistan (it was more than a few years ago!!)
Point being, I wouldn't have wanted to START building wheels on those expensive sets.
Basically, it's easy with a little practice and the right tools (I used my CDT GCSE to design and build a wheel jig since I couldn't afford a proper one)
As mentioned above, the sideways movement is easy to correct, the difficult bit is getting it cocentric.
I haven't built a wheel for 14 years, and when I came to re-tension my road bike's rear wheel (which was in a dire state), I struggled a little getting it right without making it "egg-shaped"
Its definitely a skill worth teaching yourself - but don't use top-notch kit to learn on. I'd suggest scrounging a pair of old wheels and re-lacing them, doing the front first, then moving onto the rear and worrying about dishing.
Oh - another thing that you might overlook..
Once it's done, and perfectly true in all dimensions, hold the wheel against your waist, with hands holding the rim at the opposite side, then try (not too hard) to "bend" the rim. The music of spokes pinging into place (they kind of "nest" where they cross) will be heard, then your wheel will have a little wobble again, and it's time to repeat the truing process.
Seems gutting to get it near-perfect then ping it all "out of shape" but if you don't, as soon as you put it on the bike and apply pressure to the pedals, you'll start hearing spokes go "ping" at that point.