Laying vinyl tile around a toilet is a similar process to laying ceramic or porcelain tile around a toilet, but actually a little easier because vinyl can be cut with a utility knife. Technically, you don't tile around the toilet, but under it, cutting the tiles to fit around the edge of the floor drain and setting the toilet base over it. This covers the cut edges of the tiles, so you don't have to make them perfect.
Pull the toilet by turning off and disconnecting the water line to it, then unscrewing the two floor bolts at the base with your wrench. Prepare the floor for tiling, pulling up any previous tile, carpeting or obstructions and making sure the subfloor is solid and clean.
Divide the floor into four squares using your chalk snapline, snapping two lines that intersect in the middle of the room.
Spread adhesive over the middle of the floor, covering the intersection of the two lines (you'll still be able to see the lines through the adhesive). Press your tiles into place, starting at the intersection and working your way outward along the lines, spreading more adhesive as needed. Lay all the full tiles that will fit on the floor. Let them set overnight.
Make a template of the toilet floor drain, by tracing the outer edge of the circle on a piece of tracing paper, then using that to cut a cardboard circle the size of the drain.
Lay full tiles over the toilet drain, in the position they will be in relation to the surrounding tiles. Lay your template over the tiles in the position of the drain. Trace around the template and onto the tiles. Cut the tiles with your utility knife along the curved lines you marked.
Spread adhesive on the untiled floor about the toilet drain and set your cut tiles in place. Re-install the toilet.
Ventilate the room when applying the adhesive.