It's really not terribly complex at all. The mechanics of derrailleurs (i.e., hooking up cables and adjusting the der itself), inserting seat tubes, etc., are bone-simple. The finer points of adjusting your drivetrain might take some time to learn if you don't already, but assembling a bike from scratch isn't rocket science at all.
Building a bike from scratch really won't save you much (if any) money however - if you're buying everything new. In many cases it could end up costing more. Buying used on eBay and Craigslist can help mitigate this to a very large extent, but you just have to buy with knowledge and the risk involved is a bit higher if you're inexperienced with what to look for in used equipment.
I agree completely with the previous post in the satisfaction you get from building a custom bike. Another big benefit is being able to completely customize the bike exactly the way you want it. You get to pick the exact headset, handlebars, seatpost, tires, fork, etc. In that sense, it beats buying a pre-packaged bike with some great components and then a mix of other lower-line components (such as headset, handlebars, brake calipers, hubs, etc.).
You can often score big-time on a complete bike that's slightly used though (eBay and Craigslist). Again though, you just have to be wise. Go to eBay this morning (Monday the 18th) and do a search for "Specialized S-Works" and you'll pull up a ton of duplicate entries from people with little to no feedback, separate auctions from different sellers, but who are using the same photo as the other guy along with identical descriptions (all the while having little to no feedback - for all I know they're the exact same person) and are quite clearly frauds. However, in the middle of them are a few sellers who appear in absolutely every area to be valid and honest sellers. You just have to be wise.
I scored a 9-speed Ultegra groupo on eBay a couple of months ago for $440, compared to the [almost] $1K that it'll cost new. Had less than 300 miles on it and works beautifully. Just be wise in shopping. If it sounds too good to be true, it just might be.