You'll want to remove all glue, dirt and existing mortar before you start laying your new tile floor. The floor should be completely clean in order for maximum bonding between the tile and the thinset. TSP, or trisodium phosphate, is a great all-purpose cleaner if you need to use it. It cleans extremely effectively, but is no longer as widely used today as it was before because of environmental concerns. Most people decide to lay tile from the center of the room outward, which is important if you're dealing with even-sized tiles. This method will create a nice effect in the center of the room, but tiles in the edges of the room will need to be cut. You may decide to start tiling from another spot in the room, especially if you're using irregular-sized tiles. You may choose to have uncut tiles on the sides of the room and work from there if cabinets, sofas, or other furniture is covering tiles on one side of the room. This article will assume that you want to start from the center of the room and work outward. Make sure you do a dry layout with your tile and spacers directly on the cement board before you lay down the mortar. A dry layout will allow you to visualize the room as it might be when everything is finished. Experiment with different layouts until the right one catches your eye. Set up your chalk string in the center of each wall by measuring the wall and putting the string exactly in the middle. Leave the string in place after you snap it to use as a guide for your first few tiles. Lay down some floor tiles along one of the center lines to make sure you marked the center of the room properly. If you realize that your chalk lines aren't square, redo them now. When you're laying the tile, alternate which box you're pulling from to account for any variation in color among the boxes. If you're making a design or pattern with the tile, put the tiles in order so you know which ones you need at any specific time. If you end with a very small or very large space in comparison with the size of the tile you're using, move everything down so the extra space is about the width of a half a piece of tile and snap new chalk lines to use when placing the tiles. You don't want to have to cut your tile into small pieces to finish a row along the wall.

Summary:
If you need to, clean the existing floor thoroughly with a non-toxic floor cleaner. Decide where you want to start your tile. Find the center of the room by snapping a chalk line in the center of the room widthwise and lengthwise. Line up your boxes of tile and open each one.