Usually, you will be able to tell if an improved terrain tile is connected by looking at the map. If you are not sure, place the mouse cursor over the tile and look at the text in the upper right portion of the screen. You can also info-click on the tile (right-click or shift-click) for more detailed information.  The dialog box that appears when you info-click allows you to compare production level  (how many units of resources the tile is producing) with transport level (how many units are being moved to the capital each turn). 

A tile that is unconnected has a transport level of 0. At the beginning of the game your roads can move only one unit of resources from each tile, so your transport level for a connected tile is 1.