I have a year 2000 house in Bay Area California. The Honeywell RTH2520 thermostat that came with the house doesn't work anymore because the metal things on the side of the AA batteries became aqua colored and corroded. So I'm replacing it with a Honeywell RTHL2310B. This new thermostat asks me to flip a switch to gas or electric. I looked at the back of the old one and it doesn't have a switch at all. I don't know which type of heating/cooling I have in my house. How to I figure out?
Actually, the old thermostat DOES have a "gas/electric heat" jumper. It's labeled "JP2" and the "HG" setting is for gas. The "HE" setting is for electric. It appears to be the exact same thing, just poorly labeled.
Look closely (don't touch) and its setting should be apparent.
A Google search revealed the manual in PDF as the #1 result and section 2.4 discusses the JP2 jumper.
P.S. Another way to find out if you have electric heat is go to your electric service panel and look at the labels on the breakers. For electric heat, it would be one of the large (double-wide) breakers. Turn the breaker off and see if your heat still works. The thermostat should continue to work, because it is fed from a 120V circuit (which uses a single-wide breaker).
If the breakers are not labeled, you know electric heat must be a double-breaker. You can find it by trial and error. Generally it won't do any harm to turn a double-breaker off. They control a single device: air conditioner, water heater, and the like. That device will stop working and that is all. I would label what you can.
(now in older homes or ones with well-wired outbuildings, sometimes a double breaker actually feeds a sub-panel, which has many other things running off it. I don't see that as likely in a new-build California home.)
Have you ever ventured into the basement? Do you have access to it, or someone else owns that part? If not, and you bought the house, the heating description will be in your purchase disclosure. You could ask your realtor for it if you can't find it and it was a recent purchase. If you can access the basement, you'll have some options. If there is NO furnace (nothing with big vents or lots of pipes coming out of a single 'box'), and you have many baseboard heaters, with perhaps a box that sites outside your house that looks like an air conditioner that has hoses that go into the house? Then Electric. If you have a furnace, does a little thin bendable tube come to the furnace from the outside (or inside) tank? That would be an oil furnace. Or, do heavy thick and sturdy pipes with shut-off valves go to the furnace from a meter outside? Then that's gas!
Your question: "How do I figure out what type of heating is in my home"
Answer: There are two types of heating solutions: radiant heating and forces air heating. From my understanding radiant heating does not use the type of thermostat you have. So you have a forces air heating system. This means there is a furnace somewhere in your home. This should be installed on the lowest floor in your home. Locate the furnace and examine it. While it's running, if you seem flames or light coming from it, it's a gas furnace. If not, then look at the pipes/lines connected to it. Posting a picture would be best. If you cannot, then if there is an iron or flexible pipe connected to your furnace, this is a gas line and therefore a gas furnace. Otherwise it's probably electric. But since you said your gas bill spikes in the winter, you have a gas furnace unless you have a gas fireplace that you run during the winter.