There are a great number of DIY antenna projects to be found online, try a Google search on 'DIY 70cm Omni"
The 70cm amatuer band is very close to the 434Mhz ISM band, omni is short for omni directional.
For car chasing, its a whole lot easier to buy a commercial magnetic mount antenna, try a google search for '70cm mag mount'
As for the;
"With the small antenna, I have a very poor range of only a few hundred meters"
That might be normal, you don't say what the antenna actually is or where the few hundred metres are.
Do appreciate that there is a very large differance in communications at UHF (434Mhz) between line of sight such as ground to balloon and between TX and RX at ground level, see here for some real world results;