I've heard a lot of people who sew or do their own upholstery tell me they will never "do" vinyl fabric or leather because if you make a mistake, you're stuck with it. My response to this is that if you have a project you'd like to use vinyl on, by all means give it a shot, but the key to working with it is to be as prepared as possible before you begin working with it. Actually, this is good advice for any project, but especially when it comes to working with vinyl or leather. I'd recommend trying out techniques on an inexpensive or scrap piece first. Once you get used to the feel of it, you can move on to bigger and more expensive materials.
Now, with upholstery, using vinyl fabric for basic things like bench cushions is a snap, especially if you do not intend to remove the cover once its in place.
If this is a used seat, you might need to remove the old material. If it's stapled down, use something flat like a flathead screwdriver to pry the fasters or staples up. Be cautious as you do this! Check the existing padding. Is it adequate? Do you need to add foam or batting? Consider how soft you want the seat to be. You have choices on how to add more cushion. Upholstery batting is usually made of cotton and very dense, but it isn't well bonded and so it tends to go all over the place. Polyester batting (like the kind you would use in quilting) is bonded, so it tends not to shed or flake apart. It comes in different densities and you can keep adding layers until you get the desired thickness. There's also foam, which comes in different densities and thicknesses. Your local fabric shop or foam store will be able to help you determine what is best for your project. One trick I've used is adding foam and then wrapping polyester batting over the foam. Then I add the outside material to finish it off.
Once your bench is prepped, staple your vinyl fabric down to the underside just as you would with regular fabric. Starting with one end in the center, tack down the opposite end, in the center. Then work your way out towards the sides. Finally tack the sides down as well using the same method. Decorative tacks can be used as well, but for the areas that won't be visible, I recommend a staple gun.
More about finishing off Vinyl Fabric
Be sure to use a vinyl fabric that is strong enough to handle the stress. If you need to sew the vinyl, you will find that it becomes a little bit trickier. Vinyl fabric is not forgiving when holes are punched into it with a needle. So if your seam takes in too much, for example, you cannot rip it out and "do over" because you'll have a row of holes where the needle made the first seam. However, if you need to "take it in," you'll be fine because you'll be sewing beyond the holes and they'll never be noticed on the right side.
This also means that you can pin your vinyl with heavy duty pins, but you must make sure your pin holes are within the seam allowance or else they will show up on the finished side. I recommend heavier duty quilting pins for this, and be careful! This requires a little bit of muscle.
Get a professional Look
There are things you can do to make vinyl appear more leather-like and professionally finished. For example, topstitching adds support and a finished appearance. I recommend using upholstery thread or (even better) topstitching thread for this purpose. Use finishing tacks along the edge of an upholstered piece. Metal snaps or buckles also add a "store bought" appearance. Another trick I've learned is to cover my vinyl seams with another fabric. For example, I made a bias cut trim from some faux suede for a Halloween costume. Once I had sewn my project, I wanted to give it a more polished look. So I added my faux suede trim over the vinyl seams, top stitching it 1/8th of an inch from the edge. It came out looking really good! The 7 year old I was sewing for probably had no idea how much effort went into his boots, but he had a great evening, and that was all that mattered to me. Plus I had a chance to see my prototype pattern in action.
As with anything, you'll only get as far as you are willing to go. You can work with vinyl like a pro as long as you believe in yourself and are willing to practice.