It’s often possible to do it more quickly
I’ve replaced the trackpad on my Mid-2010 15” MacBook Pro two or three times. But because my trackpad’s ribbon cable has never been damaged (my trackpad damage was always caused by liquid spills), I’ve never needed to use the lengthy process that has been posted by @bfrosty and by @mrwhitesf.
Here’s how I do it:
1) Shut down the computer
2) Remove the 10 screws from the bottom of laptop. (Using a Phillips 00 screwdriver.) Remove the bottom of the laptop.
3) Remove the 3 screws holding the battery. (Using a tri-lobe screwdriver.) I think I remember, from the first time I did this, that the screw that is closest to the hard drive was initially hidden under tape or something.
4) Lift the battery PARTWAY by pulling on the plastic tab. Then unplug the battery by sliding out the dark plastic plug from the metal socket. I use my fingernails. Remove the battery. The trackpad is underneath.
5) Because my trackpad’s ribbon cable isn’t damaged, I leave it installed and unplug the trackpad from it by sliding the exposed end of the ribbon cable towards the RAM (that is, away from the front edge). If I do this carefully, I avoid a lengthy repair.
6) Remove the four silvery screws from the trackpad. (Using a Phillips 00 screwdriver.) Remove the trackpad towards the screen. (It does not come out through the bottom of the laptop.)
7) Install the new trackpad and tighten the screws just enough so that there is a little friction to keep it from sliding around easily. Look at the front side of the trackpad and center it. Then tighten the screws fully, which doesn’t take much torque. (Too much torque can damage the screw heads.) Bending the tabs adjusts the height of the trackpad. If the trackpad sticks up too far, I’ve been able to pop it down later.
8) Attach the trackpad’s ribbon cable.
9) Plug in the battery cable (tightly, so that the battery doesn’t catch on it), lower the battery in, and put the screws in. (I put electrical tape across the screw that is closest to the hard drive.)
10) Attach the bottom cover.