How do you extract the info from an RF Rx module (like garage door opener) ?

Many of the low-cost RX modules have no filter on their outputs, so you get noise when there's no signal. You need to provide a filter. How elaborate a filter, is up to you. It also depends on the data format you use. Typically, the highest frequency in the output will be half the bit rate (ie a string of alternating 1's & 0's). That sets your filter cutoff. This won't guarantee to exclude noise, but it will set an upper limit on the rate those interrupts can occur. So long as your CPU can handle that, & you then validate the data by software, it will work.

Exactly. While there is no signal, there is only noise. I'm assuming these devices include a slicer of some kind. When RSSI drops down to the noise floor, the slice threshold falls quite rapidly until the slicer starts chewing on noise and wiggling its output randomly.

Is this where a dsp chip would be useful ? Like the dsPIC from microchip. The filter and decoding could be done in the same chip ?

How do you calculate the bit rate ? The stream of pulses (010101000) is not of equal period. There is a header where is 1ms on and 1 ms off. Then there is the data that is 2ms on and 1 ms off.

Thanks

You MEASURE the bit rate. The transmitter data rate will vary according to range [somewhat, due to slicer vagaries], battery level, temperature, etc. The preamble (the "header") allows you to measure the timing of the incoming signal.

A DSP is NOT necessary by any stretch of the imagination.