Is this a prebuilt system such as a dell, hp? If so, give the model and we can help.
If this is a built system by you or a local computer store you should be able to identify the motherboard by its labeling directly on the motherboard. Some cheaper boards don't have clear markings but its worth the effort to look anyway. You will also need to identify if its a micro atx or standard atx motherboard. Measure its width and length and post with your info if you can't find any labeling on it. As graywolf mentioned, you can get the info from the top of the cpu to help us identify your cpu socket type. This will help greatly if you can't identify the mobo...
How does one find older motherboards to match older processors.It seems such a waste with the cost of some processors.
If this is a general question not aimed at finding a specific motherboard for a specific processor, the I suggest the following steps:
1. Identify the processor you want to match with a motherboard ( physical inspection on the CPU label). You need to know the manufacturer and model name for use in searching more info for it.
2. Use google to search "motherboard"+"for"+type your CPU identity here.
3. If #2 does not give any good result, google the processor to determine the socket type ( AM2, AM2+, 775, or even older... )
4. Go to newegg or other online stores and search for motherboard that supports the given socket type.
5. Choose among the available motherboards and go to the manufacturer's website to check CPU support list to confirm that the CPU is indeed supported.