Wait a while for the engine to warm up
Your engine is warm enough to start driving in the vast majority of cars, and in the vast majority of climates, within around 30 seconds (basically, when your idle drops down to normal). That does NOT, however, mean you should just take off down the road, because the rest of your cars fluids (in your transmission and differential, for example) are still cold. For reasons related to pollution controls, your engine emits less greenhouse gasses when both the engine and exhaust components are hot.
TL/DR? Start driving after 30 seconds unless you're in an absurdly cold climate. Just don’t drive hard for the first five to 10 miles -- but you can fudge this a bit if you’re somewhere hot as hell like Phoenix in August.
Push down on the accelerator while starting your car
A long, long time ago, there was something called a carburetor. Its job was to link to your accelerator and control the amount of air and fuel that entered the engine. If your car was having a hard time starting, pushing your foot down would get a little more fuel into the combustion chamber, where (hopefully) the spark plug did its trick and ignited the mixture, starting the engine.
A slightly less-long time ago but still pretty far back into yore, fuel-injection systems took over that process. Today? Both are outdated. On most cars you don’t even control how long you crank the starter with a start button -- the button itself initiates an entire sequence of events, from squirting the right amount of fuel, to spinning the starter for the right length of time, to adding the right amount of spark. Problem solved -- human input not needed.