You just need a telescope with a "wedge" mount, (ie one for polar coordinates,) and not one which is simply a pan-and-tilt mount like commonly used for cameras. (BUT, it might be more fun to do it with a sextant -- see below.)
With a telescope that has a polar mount, you just need to set it up correctly. That means orienting the base of the mount in the correct north/south direction, and then setting the "wedge" angle to account for your geographic latitude. (Any amateur level scope with a polar mount will have instructions.) When you pan the scope it will sweep celestial lines of equal latitude, and when you tilt the scope it will sweep celestial lines of equal longitude. Point the scope at your target, and read the declination from the scope's mount.
The hardest part is going to be that the satellite will be moving pretty fast, and its orbit is going to have a continuously varying declination. (Unless you target a satellite in a circular, equatorial orbit. :)
Fun with a sextant
It might be easier to "shoot" the satellite with a simple (search for "Davis Mark 15" on ebay) sextant and something called an "artificial horizon." You need any liquid reflecting surface... a swimming pool or kiddie pool might work for shooting a moving satellite. (You can buy a small "artificial horizon" that's a few inches square, but you'll never catch the satellite's reflection in that.) Using the sextant you measure the angle between the satellite and its reflection, also noting the compass direction. Then you crunch a bunch of trigonometry. But this is exactly how you practice astronomical navigation star sighting on land.