When you get a nose bleed, often your first reaction is to tilt your head back, but this is a bad idea. Not only does this make the blood flow more rapidly when you bring your head back down, but you could also end up swallowing and the blood will end up trickling down your throat, because the nose and throat are connected.
The best thing to do is actually to hold your head down because the blood will begin to clot around the nostril.
This will take time, however, and a ruined t-shirt, so to help stop the bleed more quickly, you should get a thin flannel or cloth and rinse it under cold water, before holding it to your nose. Do not use hot or warm water as that will make the blood flow more quickly. The cold inhibits the flow.
It is also best not to use tissues, because they become saturated too quickly.
Another option is to fill a cup with cold water and dip you nose in it for several seconds. This will also inhibit the flow. Be sure to hold your breath, otherwise you'll end up breathing up the water.