I can give you a few comments, but we need an expert to check the comments and add the rest. As usual, I have to assume you know nothing, so don't take offense if this gets too elementary.
In most homes, there is a subfloor made of 3/4" CDX plywood applied over the floorjoists. Most floor coverings add another 1/2 of material over that. In order to maintain a smooth level walking surface as you move from one finish to another, linoleum needs to be applied over an "underlayment" usually either made of particle board or a smooth plywood. This needs to be set over the subfloor using screws, and the screws should be set flush with the surface. The final surface of the underlayment must be completely smooth, or any imperfections will telegraph through the linoleum. To smooth the finish, some people use a product called "fixall" which is a very hard plaster and can be found in most paint stores. As you can tell by now, this is a project you want to do one time and one time only. Do NOT buy the vinyl based on price. Buy a high grade or premium vinyl based on what you like. Keep in mind that lots of texture in the surface makes it harder to clean, but also hides some scuff marks and damage. When you go to cut your vinyl to the room, make sure that every dimension of the vinyl should be at least 3 inches bigger than the finish floor. You will go back and trim this with a utility knife later. You will need a trowel that has a toothed edge, to apply the adhesive with, your flooring sales man will happily sell one to you. You should also consider renting a floor roller, which is basically a 30# rolling pin with a long handle. This is to press the air pockets out of the floor. After rolling the vinyl which ever direction is easiest to apply to the room, start by applying adhesive in a 1 foot strip, beginning along the wall of the room where the roll starts. Set the vinyl here first, making absolutely certain that the pattern is square to the room. Spread another stripe of adhesive right next to the first, and unroll the roll a bit more, making sure to press all bubbles, wrinkles and the like out of the way. After you get the whole floor installed, trim the vinyl around at the edges, and install baseboard to hide the edge.
You could also purchase a home improvement guide, Ortho and Sunset are both very good publishers of these types of books. They have lots of pictures, which I think help a lot.
Some hints about this, 1)wear OLD clothes, the adhesive will be on them for life. 2)DO NOT put your washer and dryer in the room for at least 2 weeks. When you do, place (a lot) of cardboard on the floor (not under the appliances once they're installed, just to get them there...)and do EVERYTHING you can to protect it. Your new floor will be very soft for at least a month. 3) when you go to reconnect your hoses on your washer, replace the washers on the hoses, clean the water screens, and use flexible METAL dryer vent. Clean out your dryer while you're at it.