For HP, it should be F11 at POST, just press this key at power on. If it doesn't work, probably the previous owner already deleted recovery partition for this laptop.
You only option is contact HP and order Recovery DVD if it'a available. Otherwise, you have to fresh install OS . Be careful of OS as you have to find drivers, if it's for XP and you install Vista, you may have problem to find drivers on HP download website.
You should look on HP support website for specifications of your model.