Here's a great photo for illustrating how an internal wastegate works since all the components are shown clearly:

Exhaust gas enters the compressor chamber via the flange shown on the bottom left.
The "flapper valve" on its right is the wastegate valve. On the bottom right you can see the rod that pivots it open and closed, as well as where the wastegate actuator's shaft attaches to it so that the shaft can be rotated (opening and closing the valve).
Normally the wastegate valve is shut so ALL exhaust gas flows into the turbo's exhaust chamber which spools the compressor wheel; the air then exits the compressor chamber into the dump pipe which attaches to the flange facing you in the picture above.
When the wastegate valve opens, some of that incoming exhaust gas can exit directly into the dump pipe so the turbo will not continue to spool up as fast and will slow down if the wastegate opens enough.
Mild boost creep issues on low-boost turbos can be solved by porting the exhaust housing's channel to the wastegate valve:

In the middle you can sort-of see the face of the wastegate valve. Here the DIYer has used a grinder to create a smoother airflow to the wastegate outlet. Air tends to flow along walls so will mostly rush over the 90* wastegate outlet without this at no-to-low boost levels (at high boost levels this is less of an issue since the added pressure means it's easier for the air to flow out the wastegate outlet than into the highly pressurised compression chamber - this is why the advice "To avoid boost creep, increase your boost level!" exists; unfortunately if you only want low boost levels, this does not apply).
If your wastegate valve is seized shut, the turbo will continue spooling as the exhaust gas pressure increases - there will be a ceiling but it will be MUCH higher than the 12-14psi celing typically used with MSM/SE IHI turbos.
Another nice picture, courtesy of mazda-speed.com's
mr_hyde:
