Step One - Demolition
The first thing you need to do is remove the base boards and the toilet. To remove the toilet, shut off the water supply and flush the toilet several times to empty as much water as possible. Disconnect the supply hose and make sure water is not dripping from the shut off. Then remove the two nuts which hold the toilet bowl to the floor and save in a place you can find later. The toilet might act stick when you first try to remove it. Just gently rock it side to side until it feels loose. Then, with some help, pick it straight up and store somewhere safe.
3 Circular Saw
After you remove the base boards, it's time to remove that old nasty vinyl floor. Usually under the vinyl is a layer of particle board. This is usually 1/2" thick. The vinyl and particle board need to be removed. If you have a pedestal sink, you need to remove that prior to removing the vinyl floor. If you have a cabinet, use a reciprocating saw to cut as close to the cabinet and cabinet toe kick as possible. It's easier to leave the cabinet in than to remove it, the sink, and the faucet.
Use two crow bars to remove the particle board. It tends to come up in small chunks, but just keep at it and you'll eventually get it up. Then pull the nails that didn't come up with the particle board.
Step Two - Floor Preparation
Your sub-floor will either be plywood or tongue and groove boards. If you have plywood sub-floor, you can lay the cement board directly over that. If your sub-floor is tongue and groove wood boards, you need to install a layer of 1/2" CDX plywood over that sub-floor before you lay the cement board.
Use 1/4" cement board over the plywood sub-floor. There are several brands available, but they all work well. Some types can be cut using a regular circular saw with a carbide blade. This brand is known as Hardi-Backer. I prefer this type. The other brand (Wonderboard) is cut by scoring it with a utility knife and breaking it like sheetrock.
Mix some thin set mortar in a five gallon bucket per the mixing instructions on the bag. Using a drill motor and a mixing paddle makes this job much easier. Take a trowel with 1/4"x 1/4" notches and spread the thinset in the area where the first panel of cement board will lay. Place the cement board over the thin set and screw it down with Hardi-Backer screws. The spacing should be no more than 12" apart every direction. A trick to make this easier is to lay the cement board down on the sub-floor before you apply thin set and draw around the edges of the board so you know exactly the area to apply thin set to.
Step Three - Lay the Tile
If you don't own a tile saw, you can either borrow one from someone you know, or rent one. If you rent a saw, you can reduce the cost of renting it by laying out your floor and marking your cuts prior to renting the saw.
The first thing you need to do is determine how large your tiles will be including the grout joints. It's up to you how wide your grout joints will be. Most grout joints are 1/4" to 1/8". Lay out 10 tiles with spacers and measure the total length. Divide the total length by 10 and that will be your exact tile area with grout.
If you can, it's good to start with a full tile at large openings or doorways, but before you commit to that, check and see what size of cut you'll end up with at the other end. If it's too small, say less than 2", you'll need to cut the first tile (at the doorway) so you end up with a larger cut at the other end of the room. Measure the total distance from where the tiles start to where they end. Divide that measurement by the tile size (with grout). Take the remainder (the numbers after the decimal point), add one tile dimension to it, then divide that number by 2. That's the width of the first tile. Here's an example. Let's say you measure from your doorway to the back wall and you get 125.5". And your tiles are 12.25 inches with grout. You divide 125.5 by 12.25 and you get 10.245. You take the fraction.245 and add one tile size to it. 0.245+ 12.25= 12.49". Then you divide that by 2 and get 6.245" or 6-1/4". That's the width you would cut your first tile. And that's about what your last tile should be.
Next you're going to layout the entire floor in a grid pattern. Each grid will be equal to 4 tiles. A grid is two tiles wide by two tiles long. So if your tile size with grout is 12.25 inches, each grid will be 24.5" x 24.5". Make sure the perpendicular lines are square with each other. You can use the 3-4-5 method, or a large framing square. The 3-4-5 method is 3' one direction from a point, 4' approximately ninety degrees from the same point, and 5' diagonally from the ends of the other two lines. It's like a right triangle with a 3' side, a 4' side and the diagonal is 5'.
The next thing to do is mix some thin set mortar like you did with the hardi-backer. Using the same trowel, spread thin set in one "box" or grid at a time, making sure you can see the lines you snapped. Lay the four tiles in that grid, keeping the tiles half the grout joint width from the lines around the perimeter. You'll need to cut some tiles around cabinets, next to walls, and around the toilet. Make all your cuts first, then lay the tiles.
Step Four - Grout
Grouting is much easier and faster than laying the tile. You just mix up the grout as prescribed on the bag and,using a rubber grout float, spread the grout around and press it into the gaps between the tiles. You need to wait at least over night after you lay the tiles before you grout. Once you have filled the joints and scraped away the excess grout, let it set for 10-15 minutes then take a sponge and a bucket of water, and wipe the grout off the tiles. The sponge should be damp, not dripping wet. Rub gently in a circular motion and rinse the sponge frequently.
If your grout joints are 1/8" or wider, you'll need to use sanded grout. Non sanded grout is for grout joints less than 1/8" wide.