Start by reading this thread:
Hit in eye with 1000mw 445nm blue laser.
Did you read it? Don't just skim over it. The injury (and the aftermath thereof) in that thread is real; it happened to a real person and the person involved was
not a "noob". Think about that for a minute - if you have an accident, or lose control of your laser, or don't think things through, or just generally screw up badly, that could happen to you - or ANY one of us.
Don't let that put you off - you just want to get into the right mindset from the get-go, and admitting you're a laser noob, and not being ashamed or bothered by that means you're already on the right track.
Basically, read up on the hazards and what can go wrong - things like unexpected reflections from objects you didn't know were there; things your safety goggles won't protect you from - e.g. the IR emission from unfiltered DPSS lasers. I notice you asked about batteries, hell, you have to worry about exploding batteries, it's something to avoid. See the link in my signature for info on that.
The best part about lasers is that despite the above, they can still be enjoyed safely.
In terms of builds if you want a cheap-and-easy laser I would get the unmarked C6 from Survival Lasers (for some strange reason the marked C6 does not include the pill or brass ring) and the basic aluminum heatsink. You can order a battery contact board or not; if not then it's easy to make one out of perfboard, or cardboard, or plastic, or anything solid, non-conductive, and flat. Then, a metal object for the contact itself, a thumbtack would work.
For your diode, DTR has lots of options. The cheapest is probably the 650nm diode which, although not shown on the website, you can get with a pre-set driver if you contact DTR via PM and ask nicely.
If you want to really go cheap (but low power) AixiZ sells some inexpensive driver/diode/module combinations that will work.
Probably will want a glass lens; the 3-element is cheapest. Make sure to get the one with the right AR coating.
You will have to solder a bit. Don't let it put you off, and don't worry about shaky hands. It just takes a bit of practice... try it with some scrap wire. With the pre-assembled drivers, you're just soldering wires to the battery contacts, the sensitive stuff is already handled. Good for a first build, or if you just want a laser. You can get into the harder stuff later.
All of these people/companies are top-notch; DTR is a member here, and the people running those companies are also members. There are lots more... browse the b/s/t forum (mind the rules though!) and the laser pro shop sub-forums and you'll get an idea of what can be done and who can do it.
Use the forum search feature as well. The google search is iffy (it includes signature text in results) but it's OK for most things. The vbulletin search page might give more specific resuts.
If there is anything in this post you did not understand, or if something was mentioned and you don't know what it is, use the forum searches and see if you can find out. More than likely you'll find the info. But if not, feel free to ask questions. In most cases you can ask a question and people will just answer it, especially if you did search and can ask a better-directed, more specific question relating to your circumstances, rather than a very general question. Perhaps some future member will have the same problem you did, will search the forum and find your thread, and solve the problem.
Honestly though, I would rather ask a question and risk looking dumb than make a mistake and look (and feel) even dumber. This goes back to safety and whatnot. That, and saving money - if I had searched the forums (or asked...) maybe I wouldn't have run that flexdrive without a load - did you know it's bad to do that? Instead I got to pay for a new driver.
In regards to the question, is it like building a PC? There are standard parts - the 12mm module (aka AixiZ module) is essentially a standard, as is the M9x0.5 threaded lens assembly. Batteries are standard sizes (18650, RCR123, etc.). You have your choice of laser diodes, and laser drivers, and as long your diode and driver are compatible then the laser will work provided the driver is set up correctly. The G1/G2 lenses are the de facto standard for a high-NA aspheric collimator. The case can be standard (C6, S4, 501b) or custom. So it is kind of like building a PC in that you can customize the build to your situation and have control over what parts go into it.
Not all laser parts are compatible but neither are all computer parts. You just need to know what works with what, and what DOESN'T work with what.
Didn't mean that to be so long but that is my advice since you're interested in lasers and seem to be willing to think things through. Think safety, think outside the box, post your insights and solutions regarding any problems you might run into.
Post pictures, also. Size them to 800x600 or so but it's hard to post too many pictures, especially beam shots, and pictures that show how your build is put together. A laser forum without pictures would be pretty useless.
Have fun and good luck!
ETA:
Don't try to learn everything about lasers in a day - you will burn out. How to stay safe is #1 so stay on top of that; the rest (builds, electronics, optics) can be learned at your own pace, and according to your own interests.
When pointing at anything, always consider what is behind that object. Make sure the background is safe. You will not impress the judge if you tell him you were only trying to fluoresce a traffic cone, but somehow failed to notice the busy highway (or airport, or bus station, or construction site, or house) in the background.
