First, if you have original installation media for your computer, such as a Vista installation CD or an OEM QuickRestore CD, life will go much smoother if you just perform a clean installation on the new SSD and then delete the old installation off the hard drive once you're certain everything is working. Yes, this is a pain because you have to reinstall all of your programs. It's usually less painful than borking a transfer between disks, though, which does happen. That noted:
If your existing hard drive has MORE data installed than the size of the SSD, for example:
Your hard drive's capacity: 500GB
Total data on that hard drive: 290GB
Your new SSD: 256GB
290GB > 256GB = nope
...then you cannot simply move the OS over to the new drive using a transfer kit (which many retail-box SSDs will include) without doing something else, first. "Something else" might include:
1) Partition your hard drive. Instead of "C" at 500GB it might become "C" at 300GB and "D" at 200GB. Then, copy your pictures and music files from "C" to "D". If all goes well, the remaining OS, programs, games, etc. on "C" are now less than the size of your new SSD. Now you can use the transfer kit. Problem: when everything is done, your hard drive has two partitions and you probably just need one, so now you have to "undo" it. So your next option is...
2) Get an external USB hard drive and back up your pictures and music files onto it. (Really, you should be doing this anyway.) When you are certain that everything is successfully copied onto the USB hard drive, delete those files from your main hard drive, and continue with the SSD install. Afterward, you can clean-format the hard drive and move your stored files back onto it.
3) Get an online file storage account, then same as (2). I personally don't like this option but it works for some people.
He who laughs last, laughs first next time.