I would really like to know how big the squares should be on my battle map. I haven't made one yet but I am hopefully going to, and I intend to use it with miniatures for combat.
1 inch squares, corresponding to 5 feet.
The DMG suggests that you make the squares on your battle map 1 inch on each side. These squares then correspond to 5 feet for game purposes.
You can draw tactical maps with colored markers on a wet-erase vinyl mat with l-inch squares... The most common unit for tactical maps is the 5-foot square, and maps with grids are readily available and easy to create.
1 inch squares are consistent with standard D&D miniatures, which have roughly 1 inch circular bases.
They should be big enough to comfortably hold the base of your largest single tile minatures. For the most common miniature lines this is about an inch (roughly 2.5cm) on each side, but you should fit it to the scale of your miniatures.
Dungeons and Dragons has routinely used inches for its measurements, a tradition dating back to its late 70s wargaming roots. This means things will be easier on you if your battle mat has 1" squares like the Dungeon Master's Guide mentions; for example, metal and plastic miniatures in this scale are the easiest to find. That said…
This DM prefers a battle mat with 1½" (38mm) squares
For a variety of reasons—like ease of on-the-fly customization, removable accessories, and the fact that I can't paint—, I use Lego brand minifigures instead of traditional miniatures. While bigger than traditional miniatures, the bases that come with individual random minifigures still leave some room in these larger squares. (One of the problems I've had with using a traditional miniatures and 1" squares is that the mini's bases are the exact same size as the mat's squares, preventing folks from seeing the edges of images drawn on the map!)
Further, 1½" squares accommodate Mage Knight figures and other figures with larger bases that are also dials (which are often available inexpensively), and I've found these larger squares also tend to more easily accommodate plastic toys that are available at convenience stores.