1. What is an ohm? What does that mean?
An ohm is a measure of resistance. It can get pretty complicated, but here is the short version. Every speaker you connect to an amp demands more power from the amplifier. The amplifier, at least in solid-state examples, is designed to give more power but they can only give so much. If you connect 2 4-ohm cabinets to an amp that can't give more than 4 ohms, it will overheat. You will experience thermal shutdown and may cause permanent damage to the amp.
Understanding that, here is your formula. 2 8-ohm cabs will draw 4 ohms from your amp. 2 4-ohm cabs will draw 2 ohms from your amp. Every amp that I know of goes down to 4 ohms, but most do NOT go down to 2 ohms. Know your amp's minimum ohmage and do not try to draw more power from your amp than it can handle and everything will be peachy. You can learn more about this if you want, but that should be all you need to know to get by.
2. What is a "tube amp", and why must they warm up?
Tube amps use tubes for their power supply instead of solid-state transistors. Not sure why they need to warm up. I just always followed directions in that regard (i.e. let it warm up).
3. A head just connects directly into a cab, and is turned on when the head is turned on? Any random details on this would be great.
Cabs do not turn on, they don't have on/off switches. They simply react to the fact that power, from your amplifier, is being sent to them and do what they are designed to do. Just make sure that all connections (bass to amp, amp to speakers) are made before turning your amp on. That way, you avoid the loud pop that happens when plug something in after you've turned on your amp. This can wreck your speakers rather quickly.
4. What is the difference in a 1x15, 2x12, etc. except amount of sound? When making a rig, why have a 1x15 and a 2 or 4x12?
The only difference is amount and type of sound. This is a highly subjective area. Some like 10s, some like 15s, others like 12s. Some like a combination of 2 or more of each (i.e. a 2x10 and a 1x15) to get the best attributes of each kind of speaker. 15s are typically deeper-sounding, they push a lot of air, but can be muddy and indistinct. 10s are fast and give you lots of "punch", but sometimes they don't handle lows very well, especially on a 5-string or downtuned 4-string. 12's are kind of in between 15s and 10s, they are deeper than 10s, but punchier than 15s. Then again, they are not as deep as 15s or as punchy as 10s. Its all about your personal preference. I like 12s most, but also like 10s quite a bit. I don't care much for 15s.
Of course, these are generalizations. There are 10s that sound really deep and 15s that are clear as a bell. There are so many different options out there your head will spin if you try to learn them all. You've just got to learn what YOU like and what makes sense for your rig.
Hope this long-winded post helps you.