Propflying is a glitch, first discovered by DemonStrate and it is one of main transportation methods in Source engine games, most commonly used in Old Engine speedruns. The first speedrun to feature this technique was Half-Life 2 Done Quick. It is significantly more limited in the OrangeBox engine games, and as a result, other techniques such as Accelerated Back Hopping with the combination of slopes may be used instead to cover large areas over the air.
If you pick up an object while standing on it and jump, it will follow you upwards. If you repeatedly do this, you will continue to gain height. With most objects holding in the forward button helps, as it maintains your place on the object, whereas otherwise it starts to come out from under you. Flat objects with a good amount of room for standing are easiest to fly with.
In Old Engine, there are a few tricks you can use to adjust your speed and altitude.
Climbing is another flying method, used to gain height and distance, rapidly. Normally if you hold in forward while flying without letting go for a certain amount of time, eventually you'll end up gaining too much speed and flying off and past the object. However, if the object is slanted in front of you just right, you are repeatedly jumping forward off and into the object, therefore you are not only kept from flying off the end, but you jump more rapidly, as you land on the object faster. This makes for a sharper climb in height and better speed.
Crouch and stop jumping. As long as you don't do this too long, you are able to start flying again. This can also be used to keep yourself from falling off of the object.
If you are using a long flat object you can do this by jumping in place without moving. With some objects you can cause it to re-orientate by standing on the edges whilst flying. This will also allow you to gain height.
Propflying in OrangeBox Engine is much more limited. The object you are holding tends to get automatically released, or starts changing it's position so you cannot jump on it anymore while holding it. Therefore you constantly have to re-grab the object after every jump, similar to Wallclimbing. It also helps to use specific setups with objects such as barrels and supply crates.