SP Crater is located in the San Francisco Volcanic Field. "SP" literally stands for "Sh$t Pot" because with its almost perfect conical shape the lava flow seems to have spilled out on one side and the cowboys thought it looked just like... well you get the idea.
The top of the crater is at 7027'. To the west of the crater is a lower volcanic rise... a small saddle. Basically you "summit" this first then head up the SP Crater. You can do this from either the north or the south side. But keep this in mind; even though it is only about an 800' ascent, if you've ever climbed a volcano you know that it is two-to-one ratio. For every two steps up, you slide one step back. Furthermore, when you start to loose your footing you can't help but try and scurry up. So considering the altitude and the amount of physical exertion, my advice is to first ascend the southern side to get to the saddle. It is longer, but the grade is less, which will leave you with more energy to climb the crater.
Once you are on the saddle you can see a couple of trails the lead to the top. But it's real simple, just head up, all paths lead to the top. Please try to keep trail erosion to a minimum. This is the reason National Park department closed the trail that leads up to the top of nearby Sunset Crater.
The summit provides a great view of the San Francisco Peaks from the north side, the lava flow coming from the crater and the surrounding area. The volcanic field is very barren, but that just adds to the surreal look of the place and makes it all the more interesting. You are able to walk around the complete crater at the top and there is full visibility into the bottom of the crater. But I would only advise going down in the center of the crater to a certain point. After a bit it gets steep and the soil is very loose.
Descending the crater takes about fifteen minutes and is great fun. You basically take a few steps, jump, then hit the ground to a cushioned landing and do it again. But once again, do this sparingly so that erosion is kept to a minimum.
WARNING! Hiking and outdoor related sports can be dangerous. Be responsible and prepare for the trip. Study the area you are entering and plan accordingly. Dress for the current and unexpected weather changes. Take plenty of water. Never go alone. Make an itinerary with your plan(s), route(s), destination(s) and expected return time. Give your itinerary to trusted family and/or friends.