The Map tab is used for editing everything on the map. It is only available if you have the "Map Enabled" option in Settings turned on. After loading a BIQ while this setting is on, you'll notice that the MAP tab remains grayed out for awhile after the other tabs are ready. It takes a bit longer for the map tab to load, so you'll have to wait a few seconds for it to finish loading. You can safely edit the other tabs in this time, however.
The map is divided into two pieces, the map itself and a control panel of sorts on the right side. We'll give the tour based on the control panel.
The little arrow button (>) will hide the control panel, and give you more space on the map. This can be useful if, for example, you are painting terrain, or just want a bigger view. After clicking it, a < button will appear that you can click to get the control panel back.
The hand logo button is used to select tiles to bring them up in the control panel. After clicking them you can do all sorts of things - change overlays, change city names, add units, etc.
The green diamond logo button is used to paint terrain. After clicking it, you'll get a terrain selection popup, and then can click on the map (or click and drag) to paint terrain. If a terrain isn't changing, consider that you positioning may be illegal given the surrounding terrain (you can't put tundra next to desert, for example - it's a Civ3 limitation). You can also press the "t" button to get the terrain selection popup while you have the map open and aren't editing a text field such as a city name. Landmark terrains are to be supported later, but cannot be added at this point.
The bow-and-arrow logo and the starting location logo will be usable in the future to add units and overlays, but for now these must be added with the control panel.
The House icon is used to add new cities. Click on it, then click on the map to add a city. When you click on the map, you'll be asked for a name for your brand new city. You cannot add cities where a city already exists.
Below these icons are the tile view area and an area that either tells you the terrain and grid location, or lets you edit the city's name. To get the location of a city tile, you'll have to do a tiny bit of math and calculate from a neighboring tile.
Next, if applicable, comes an area to set a tile's owner. This applies when the tile has radar towers, airfields, colonies, outposts, cities, or units.
The Rivers area lets you control river layout. I always found it infuriating trying to get rivers to go where I wanted in Firaxis's editor, so this is a different way to do it. Select a tile, and then click which borders of the tile (NW, NE, SE, SW) should have rivers. No rivers unexpectedly going a different way! The buttons are also layed out in the correct directional layout, so you needn't think about which way is southeast.
The resources and overlay areas are pretty straightforward. You can't have both an Outpost and an Airfield or Colony or Radar Tower.
The Add Units area comes last. Choose the number of units, experience, and type, and then click Add - you can add a whole bunch of units easily if appropriate. Below this area is a table of the units that have already been added. You can use this table to easily modify the existing units, changing their number, experience level, or removing them all together. If you combine two different groups of units into the same type, they'll be auto-combined into one group (with the appropriate updated number of them) the next time you select the tile. It is not yet possible to individualize the units (such as giving them custom names), but any existing individualizations should remain.