I have in mind a small solar panel that could be plugged into a wall socket. Do I need a converter or some kind of interference between the two power sources so there aren't any unpleasant explosions? I don't know much about this sort of thing so please be nice.
No a solar panel puts out DC voltage like a car battery and you house uses Ac voltage generated voltage yes you need a converter to use the dc on an ac unit depends on the Amperage out put of the solar panel
You're quite right that the solar panel can't be directly connected. I sense that you want to start small, but unfortunately, it's hard enough to make a system with a dozen or more panels pay back. (It can, we have a system...) But with just one panel, maybe a small one, the economy of scale is gone. You need to buy a grid-tie inverter, which watt-for-watt will be more expensive than a regular size one, and for a small panel, the $$/watt value will be poor. There are some [illegal in most places] tiny grid-tie inverters that I see advertised on the web from time to time, with an ordinary plug that goes into the wall. Those are generally against electrical codes, and the danger is real. There is also a crop of micro-inverters being sold by companies such as Enphase. These are legitimate products, but will still be costly per watt, and ultimately, it will be hard to have a net savings over time with just one panel. Have you already taken the conservation steps like LED light bulbs, efficient appliances (especially refrigerator), insulation, and using a power strip to turn off loads that are not being used? That stuff isn't sexy, but saves money fast.
You can use a solar panel to heat water, and you can generate electricity, but you can't plug it into a wall socket. The most effective way to save on your energy bill is by heating water. Solar panels that produce electricity, don't store it. They produce it for that particular time, and if you're not there to use it, it's gone. Furthermore, the electricity isn't always regular, it may have peaks and shortages. The best way to tap into that, would be to sell the electricity you produce to the grid, and then buy it back when you use it.
The other responders have given partial information. The electricity in your house is 20 volts AC and the solar panel will produce DC voltage. If you plugged in the solar panel into the wall, the solar panel would be destroyed, possibly with disastrous results. If you connected the solar panel to a DC to AC inverter, there are also dangers. The solar panel unless very large will not produce enough power to make a lot of AC, for every amp of 20 volt AC, you require more than 0 Amps of DC voltage. So most small solar panels are used to trickle charge a 2 volt battery used in backup situation. The problem is that the house AC and the inverter AC have to be exactly in phase or again you have disastrous results. If they are exactly 80 degrees out of phase, the wires now are carrying 240 volts and you will burn out the inverter, and possibly cause a fire. There are systems that will synchronize an inverter to commercial power so that you can feed the power back to the grid, but these are more complicated. If you want to use the battery and solar panel to run some lights during power failures, then you can connect the light to the common terminals of a switch, but the switch must be a break before make switch, which means that when you throw the switch the common is disconnected from the one source before it is connected to another source. Most AC switches will do this, but make sure.
