Disconnecting the battery can cause issues.
Sometimes the engine computer relies on the battery to keep its settings. If you disconnect the battery long enough for it to lose its settings, then the car won’t run as efficiently while the computer goes back through its “learning” phase.
Your radio will likely lose all of its presets. If the radio has anti-theft protection, disconnecting the battery can cause issues with it, and you might need to take it into the dealer to do a factory reset.
Some alarm / anti-theft systems will also have issues.
If you disconnect the battery, and it won’t cause issues with your car, removing one of the terminals is sufficient. You don’t need to remove both. A lot of folks say to remove the negative terminal first, though in many cases it doesn’t make much difference. On some cars, if you remove the positive first, you can accidentally create a short between the positive terminal and the car’s body (which is electrically connected to the negative terminal) through your wrench, which is definitely not recommended. Worst case, the battery explodes in your face. If you remove the negative first and your wrench accidentally touches the car body, that’s what the negative is already connected to so no biggie.
The isolator switch that @steronz mentioned also works well and will save you some wear and tear on your battery terminals.
A trickle charger works well. You don’t need to disconnect the battery.
You should drive the car about once a month, long enough for the engine to fully reach its operating temperature. If you don’t let the engine get up to temperature, then water that has condensed in the engine will stay there and contaminate your oil, and water from engine combustion will settle in your exhaust system, causing it to rust and die an early death. If you get everything up to temperature, then the water gets flashed into steam and expelled from the car.
Your tires can develop flat spots from sitting. In my experience these usually work their way out on their own after a couple of weeks of daily driving, but you might want to lift the car up onto jack stands to keep the tires from developing flat spots.
You need to drive the car enough to go through a tank of gas every six months or so, otherwise the gas can start to go bad. Your car will probably run on year-old gas, but it will likely run a bit rough.