We visited this during our trip to Segovia over Christmas. Initially, we walked around the outside of the Alcazar, using the path that winds round the rock on which it stands. There is a nice walk through woodlands that starts at the edge of the city walls and then continues downhill to some pleasant gardens and woodland. You get to see a different aspect of the Alcazar (and see some nice churches en route too). Once out of the woodland, you do have to walk uphill again, which is a bit of a pull, but worth it for the views over the Alcazar and over the plains around Segovia.
The actual Alcazar visit offers two options: you can visit the Alcazar on its own or pay more for a ticket that allows you to go up the tower for supposedly better views. We chose the Alcazar by itself, as I felt I'd had quite enough of walking up things for the day. There is also an audio guide that you can buy. The interior is interesting, with several notable rooms, particularly the room with an excellent selection of armour on display. The Hall of Kings has portraits of all the Spanish nobility, but the significance of this may be lost of non-students of Spanish history.
Much of the castle was restored in the 19th century, so what you're seeing isn't 'authentic' in the sense of being very ancient, but it's well done and still very interesting. There's also a small exhibition showing the history of the military academy that was housed there for some years. This is mostly in Spanish, but a good insight into how the building has been used.
I think, overall, the outside of the Alcazar, when seen from a distance is the more interesting and rewarding experience. There are many beautiful interiors to be see in many places in Spain, but the sheer extravagance of the exterior (it really is the Disney castle) makes this one stand out.