How to get materials you need
from a planet that doesn't want you to have them
The simplest version of mining is to simply not include it. Games such as "Master of Orion" and "Galactic Civilizations" get along quite nicely without burdening the player with such things. This means that, essentially, research and ship/structure building are that much more difficult to make up for the reduced effort not put into mining.
Medium:
The next complexity level for mining is to have a single material: metals. This is demonstrated by the game "Spaceward Ho!". Each planet or other body will have a quantity of metals on/in them. Putting effort into mining will get the metals out (and into your storage account) at a linear rate. Ships will cost a certain amount of metal (possibly with a miniaturization technology), which comes from your account. This puts an inherent timeframe on the game, as once your metal has run out, you realy can't do anything.
Complex:
The final complexity level is the most interesting. One version of it is in the game "Stars!", from which I have drawn much other inspiration. The idea is that you have several different materials which are rare, and which you mine from your planets. Rather than the two imaginary and one real elements from "Stars!", I feel the appropriate way to split it up is by categories on the periodic table. The categories are: light metals, heavy metals, radioactives, fusibles, volatiles, organics. I might also include a "common" category, which is everything else.
Light and heavy metals are just the top and bottom regions of the metal range, respectively with the cutoff between the two around iron. Light metals are far more common, and are mostly used for construction and building things. Heavy metals are far more rare and are used for more complex purposes.
Radioactives are usually metals, are several times more rare than even heavy metals, and are used for fusion reactors and other radioactivity-based technologies (don't sneer at it; in some games that's the best available for a thousand years or more).
Fusibles are basically certain isotopes of hydrogen (2H and 3H), Helium (3He) and Lithium which are profitable to use in fusion reactors and fusion explosives. They are roughly half as rare as radioactives.
Volatiles are all of the rest of the gases (aside from fusibles), and are used for things like building new habitable settlements (You've gotta' get that air you breathe somewhere.). Volatiles are not so much "Mined" from the ground as taken from the atmosphere of planets heavy enough to hold an atmosphere. Sure, you can mine them if there isn't an easier way (as there will be a certain amount of volatiles tied up in the structure of many minerals) but that is far more expensive.
Organics are carbon-containing minerals in the ground. The main idea is to include things like petroleum and coal (which you can burn and waste, if you see fit). I could call it "hydrocarbons", but that name tends to disclude coal, which has relatively little hydrogen. The trouble with calling it "organics" is that that tends to include things like Calcium Carbonate, which you can't burn, but which are technically organic. Anyway, organics concentration will vary from game to game, but will generally be lower than light metals but higher than everything else.
Common materials include silicon, and other semiconductors, and basically everything not in a category above. If you include common minerals, then it is possible to mine away the structure of a planet completely, leaving nothing behind.
The idea of the equation for mining is that it becomes easier to mine the more experience/infrastructure you have on the planet, and harder to mine the less of a material there is left. The equation is P=a+Q(1-Q/Qt), where P is prodction (annually), Q is total produced to date, and Qt is original total available to be produced and a is a sort of investment factor, to account for money coming into the industry from outside. My modified version of the equation is P=E*(a+Q*S*(1-Q/Qt)), where E is the % of effort put into it (you might not want to bother mining as much as you can in a given year), and S is the slowdown factor, basically how much experience and technology you have for mining the particular material. The obvious way to manage the effort property is for the player to be able to put in a cap on mining; ie "I want to mine as much heavy metals as possible up to 10,000 tons per year".
Assuming you have a demand for as much of a material as you can produce, the productin graph will look like this:
And the total produced will look like this:
At that high-production zone you get the sharpest angle. As time goes to infinity, you eventually get to the point where you have produced all there is to do.
The only big modification to this pattern possible is that with certain technologies it might be that only a certain portion of the total mineral content of a planet is available from the start, and for the rest of it you need higher technologies (ie Qt in the equation above increases). This would lead to multiple peaks (if you reach one peak before you discover the next technology), or at least a discontinuity in the slope of the graph if you haven't gotten to the peak yet.