[Caduceus]

From the FAQ:

4.6.2 Remote mining uses supplies and maintenance, for this reason it is best to use bases as they have infinite supplies and reduced maintenance costs. If you use bases, you must build it with a Space Yard ship at the desired location.(Gandalph)
4.6.3 Only one Ship or Base can mine a location at once. Whichever is placed first will mine.
All mining components on a ship or base will produce, and the value of the planet or asteroids will drop exactly 1% per turn no matter how many mining components you have.(Suicide Junkie)
4.6.4 In a stack of satellites, up to three satellites can mine, provided they all have robo-miners working on different resources. Three mineral miner sats will produce the same amount of minerals as one mineral miner sat. A mineral miner sat plus a radioactives miner sat can both work on the same location at the same time, producing the full amount of both resources.(Suicide Junkie)
4.6.5 Remote mining depletes the available resources at the location. It does not happen quickly, but you will see the value of the location drop over time.(Gandalph)
4.6.8 Income generated from remote mining is not shared with your trade partners. So if you were a race that got a lot of it's income from remote mining your allies would be potentially getting less benefit from the treaty than you, even if you both had equal economies.

Mining, as I understand it, cannot be stacked. Therefore, you have to consider if you are building a base - its turn cost and how long you would have to mine a particular spot to break even. If you have that much time on your hands, it might make more sense to just turn that asteroid belt into a planet or develop Gas/Rock/Ice colonization for the planet.