Canceling into special moves can be a confusing topic for people new to the Street Fighter IV engine. For example, with Ryu the sequence MP, HP, Hadoken can combo but at first glance appears to require really quick movements. A lot of players (myself included) start by trying to press MP, HP, qcf+P in sequence as fast as possible. Occasionally it will come out but generally results in a lot of panicked button-mashing. What typically happens is an MP, HP, and then…nothing.
There are two tricks to understand here. One is that a separate punch button does not need to be pressed in order to execute the Hadoken. Rather, the HP button can be held down through the qcf (quarter-circle-forward) and then released at the end of the motion in order to execute the move. This avoids the need to push an extra punch button at the end of the sequence. The second trick is to time the Hadoken such that the HP cancels into the move. Canceling is achieved when a special move is entered prior to the previous move finishing. In this example, start the qcf motion while pressing the HP. The sequence of operations is HP (hold), qcf + release HP. By starting the qcf early you can execute the Hadoken by simply lifting off HP right as you push forward. This trick can be extended to the combo MP, HP, EX Hadoken. Press the MP and HP in rapid succession, holding both buttons down then perform the qcf and release both buttons just as the HP animation is coming out. The HP will cancel into an EX Hadoken.
The cancel means that the recovery frames of the HP don’t come out. Instead the HP animation goes directly into the Hadoken animation. Try this out by performing a standing HP and watching the start-up, active, and recovery frames. Now try starting a qcf motion prior to pressing HP and finishing it while releasing HP. If done right the HP will cancel into a Hadoken. You’ll notice that the HP recovery animation is missing. This is the essence of a cancel and is what permits the special move at the end of the chain to be part of the combo.