The gaps between tiles are traditionally filled with grout, a cement based paste available in a range of colours. The task of grouting is the easiest part of laying tiles, however, bad application can affect the finish of a tiled wall dramatically.
Grouting should be left until the tile adhesive has completely set (about 24 hours normally). Use the supplied applicator or a fine textured sponge to fill the joints between the tiles. If you are tiling anywhere near a water-source or areas that will get damp, make sure you use an epoxy-based waterproof grout. This makes cleaning much easier as well as stopping water seeping through to get behind the tiles. There are also specialist grouts for food preparation areas, although this is not really needed in your home.
Wipe off any excess with a damp sponge and use a small stick with a rounded end to “point” the grouting. You can buy special tools for this, but an old ice-lolly stick will do just as well. Leave the grout to dry for the recommended amount of time and then go back and use a slightly damp, soft cloth to polish any remaining grout from the face of the tiles.