Takes a lot of patience, and building a bike isn't easy. Requires a bunch of special equipment, some of which is component specific and may not work with your MTB or your GF's gear.
Actually, building a bike from a bare frame takes very few bike specific tools to build up and it's fairly easy.
Sure, you may need a specific bottom bracket tool to mount it....but your LBS can do it for you for a few $$ and save you from having to buy the Shimano or whatever tool you need to mount it. (Typically, there are two types of bottom bracket one encounters these days---screw in and press in.)
The rest of the bike can be built up with hex keys/wrenches, outside sizing the chain for which you'll need a chain breaker---$10-$15 or so for a decent one, and you'll need that tool, the chain breaker, more than almost any other tool you'll use, outside the hex wrenches/keys.
Oh, and you may need a cassette socket, but again, just get your LBS to mount the cassette on your wheel.....just a few $$ again.
Now you're down to needing the other specific bike tools.....tire irons to get the tire off the wheels so you can change flat tubes. Another $5 for a set of 3 plastic ones.
Not much else comes to mind. Sure, you can go all out buying Park tools for every specific bit of work, but many of the Park tools are easily replicated cheaply, such as a headset/bb bearing press. You can buy the Park tool for expensive or build up one for under $20. Pedal wrench, you say? A good longish handled adjustable wrench fills in quite well for a pedal wrench and is cheaper and more versatile.
Speaking of tires, you can find good quality roadie tires for commuting/pleasure riding for under $30/ea quite easily.
And quit trying to do the fixie crap. You'll end up in the wrong gear 95% of the time unless you live on a billiard table or somewhere just as flat.
