Depending on your laptop you should have like a panel and screws going into it. If you have multiple panels you might just have to use trial and error. Most laptops have dual channels for RAM and you'll notice its kinda stair like stacked. Easier to google it probably what it looks like for your computer. Most laptops need SODIMM RAM cards which can range from $30-$160 depending on value of RAM. You'll also want to look up the capacity of your RAM, like how much the max RAM you can use, because if you don't and buy something that is over your Max is will be useless. You'll also want to pair your RAM so don't buy like a 2GB RAM stick and a 4GB RAM stick you'll want either two 2GB or two 4GB.
Before I got into anymore detail on really how to install the RAM and what not just let me know if you are serious about this. It could be pretty lengthy.
I spent $71.00 on two 4GB RAM Sticks from Best Buy.