Altitude is part of the problem. Assuming you wanted to get to GEO from a circular, 700 km altitude orbit you'd first need to do a burn of about 2.24 km/sec along the orbital velocity direction to raise the apogee of the transfer orbit (the half-ellipse):
The spacecraft wouldn't normally do it itself, the launcher upper stage would typically inject you into a Geostationary Transfer Orbit (GTO) directly.
What every spacecraft has to do itself, however, is circularisation of the orbit once it reaches the geostationary altitude. This is done by doing yet another burn along the orbital velocity direction, but this time of 1.2 km/sec. You can think of this burn as trying to raise perigee altitude and circularising the orbit or matching the spacecraft's velocity to match the geostationary orbit's velocity. Any inclination changes are also done there to reduce the mass of the fuel necessary (the slower you go the less fuel you need to change inclination by some amount).
And that's how you get to GEO. So the problem is, by the measure of delta-V, mainly due to altitude, less so regarding the velocity. The only problem is every spacecraft has to do the circularisation burn itself, which adds some complexity.