Four stroke operation is fairly simple in theory compared to the two stroke, but it has more moving parts making it more mechanically complicated.
Stroke 1 Intake Stroke
The intake stroke does just that, it moves fresh fuel/air into the combustion chamber. While the piston is moving away from the ignition source, the intake valve is open, the piston then draws fuel air into the cylinder.
Stroke 2 Compression Stroke
The cylinder should be fully charged by the time the piston reaches BDC (bottom dead center), the Intake valve closes at BDC and the piston begins to travel towards the ignition source. This compresses the air/fuel mixture, causing it to become more volatile or flammable. Just before TDC (top dead center) the ignition source fires.
Stroke 3 Power Stroke
The ignition fired right before TDC and the piston is being forced down the cylinder by the explosion that is happening in the combustion chamber. Just before BDC the exhaust valve starts to open.
Stroke 4 Exhaust Stroke
The piston has reached BDC and the exhaust valve is partially open, When the piston begins to travel up the cylinder, the exhaust valve will completely open. The piston will push the spent gases out of the exhaust valve and the valve will close when the piston reaches TDC. This will clear the cylinder of spent air/fuel so a fresh charge of air/fuel can be drawn in by the next intake stroke.
There is some overlap with cam timing between the exhaust stroke and intake stroke. This overlap allows the momentum of the exhaust gases to start pulling fresh intake gases into the cylinder, allowing the combustion chamber to get a more complete exhaust purge. This will lead a more in depth discussion about cam timing in the future.