How to install a bigger hard drive???

You don't specify which model MBP you have, so it's hard to direct you to the right documentation for replacing the part.

One strategy for transferring the data is to install the new drive into an enclosure, clone from the old drive to the new one, then move the new drive into the machine and put the old one into the enclosure so you can continue to use it.

Is it a 17" or unibody (no user removable battery)?
If it is a 17" or unibody, is the drive SATA? If not, you got the wrong hard drive.

If not 17" or unibody, is the hard drive 9.5mm or less? If not, you got the wrong hard drive.

The manual that shipped with the machine normally has instructions. Manuals are also available on http://www.apple.com/support/ for many MacBook Pros. For the few that aren't these three sites typically have instructions:
http://www.ifixit.com/
http://www.macsales.com
http://www.xlr8yourmac.com/

As for transferring, I recommend making at least two clones in case of accident or bad drive*:

http://www.macmaps.com/backup.html

- * Links to my pages may give me compensation.

I just upgraded the hard drive in mine. I went to western digital scorpio 640 gig. Super easy. Because I use time machine to back everything up, it took me 5 minutes to install the new HD, and then two hours for time machine to completely restore my whole HD into my new 640 gig HD.

To do it, you need your OSX that came with your computer. You boot up the new HD from that disk, do a disk erase on the new one (yes, erase the new one even though it's empty, just to get it to format for you) and the OSX installs. After it installs, you go to the utilities and select restore, select your external HD where your time machine backs up, and DONE DONE DONE!! The longest bit was to restore my hard drive. Took about 90 minutes. The easiest upgrad I've ever done!!

The Seagate Momentus hybrid is 9.5mm tall and a SATA drive, so it should work in your Mac even if it is a pre-unibody 15". Since it is from 2007, it is a pre-unibody.

Look at both ifixit and powerbook medic for instructions. I don't know if Apple would install it for you, since they generally only want to install drives like the ones that originally shipped with the machine. However, if you decide you don't want to do it yourself, you could look for an AASP in your area, who could also do the cloning operation.

Is your old drive in good shape, or is it failing? If it is failing, you would be better off to install all the software fresh from discs and update it and then migrate your data. Here is a guide for doing that:

http://discussions.apple.com/thread.jspa?threadID=435350&tstart=0

You can find good enclosures at OWC. Check their clearance/garage sale page for specials. Be sure to get a SATA enclosure and not an EIDE one. Especially good are the Mercury on the Go Firewire enclosures. I have several of these and they're great!

I'm about to do the same next week with my 2007 machine, since the hard drive started going south a week after my Applecare expired.

Good luck!