My iMac 10.5.8 computer which was bought in October 2006 has been running rather slowly. "You experience poor performance in everyday tasks. For instance, a program doesn't respond or seems to take forever to open."* This is because as upgrades of software keep getting added they require more memory to run (at least I think that is the general idea). Anyhow both Alastair and the Apple store lads said "You need more memory [RAM]." Now it took me awhile to get my act together but I am here to say that I have purchased and installed the equipment successfully therefore anyone can do it!
 You buy a piece of equipment called a memory module and put it into the back of your computer replacing one of the two that are already in there. It is that green thing mid-photograph below. It is purchased from * Cruicial.com. It arrived in an envelope by post. The description on the delivery note states that it is Quantity = 1 of "Upgrade for Apple iMac 2.16 GHz Intel Core 2 Due (24-inch) System 2 GB 200-PIN DDR2 SOSDIMM 256Mx64 PC2-5300".
 To intall watch this video showing how to put it into the back of this type of "white Intel" type of iMac. (It's a shame about the hellish rock music but the demo is spot on.) There are other excellent videos which can be found by searching "upgrade Mac memory or "to install RAM in an iMac".
 With a Phillips No. 2 screwdriver and a good source of light it is exactly as described in the video.
I don't know if it matters which slot the new one goes in, i.e. I took the top one of two out and replaced it with the one which is lying on the glass table top in the photo. (It was quite difficult to get out! The white plastic side clips are stiff, as described, but snapped as they were supposed to.)
So now the MEMORY has gone from 1GB to 2.5 GB. (Screenshot on top is BEFORE; Screenshot below is AFTER.)