I have been building these as a hobby for quite a while now playing with different designs and shapes seeing what works best. If you're looking for something homemade and portable you're best bet to start off would be a yagi or a cantenna. The cantenna is the easiest to make but i've never cared too much for them because they're touchy about losing signal and its easy to knock the connections loose while you're packing/unpacking them. Yagi's are a little more tedious to build since you have to be pretty precise with the measurements of the element placements and shapes but I've got a copy of a yagi calculator that will actually print out schematics and step by step instructions for every little detail of the design for you.
My portable yagi is about 2 feet long and is essentially flat (less than 1/2" thick) and just a few inches wide. It cost me 7 bucks and change to buy all the parts for it (1/4 inch round wood dowel rod 2' long, couple feet of heavy duty copper wire, n-type connector, a few feet of connecting cord) and gets about 13.5dBi on average. Its a pseudo-directional antenna so i just have to have it oriented in the "general direction" of where the Ap is instead of having to tune the angle and pitch like most cantenna's and its many times more powerful.
Parabolic Dish setups are probably the best performers (of the ones that i have made) with a HUGE range but they're usually made of big awkward shaped satellite dishes and don't relocate very well so you'll probably not be packing one around in your car.
The best way to start out tho is to pick up an old last generation USB WiFi adapter (has to be wireless G...thats important) and plug it into a USB extension cord. Mainly because most people don't have an external antenna hookup on their laptops by default so you'll either be buying a removable slide in card adapter or you'll have to get technical and solder a couple of wires onto you're internal wifi card (the first 2 times i did that i bricked the wifi cards). You can tap into the 2 antenna wires that come from your card up into the back of your laptop screen if you prefer but they're really tough to tap into correctly and even still doing it that way kills the signal you recieve anyway by a lot.
I paid 5 bucks for >THIS USB WiFi
and used it as the reciever on a dish setup and was getting an 80 % signal from an AP over a mile away.
I'm actually working on an article to post about going into detail building a couple of different types and what kind of parts you can substitute for them that I was gonna post here in a day or so.