I like to apply my first coat of polyurethane with a 12″ drywall trowel. I usually thin the finish I use (Fabulon Brand heavy-duty poly satin) about 3-5% when I am troweling it. This particular brand has a bit too much body for troweling. In my case want to slow the drying down on this first coat, so I add odorless mineral spirits. I want to prevent trowel marks. I pour a puddle of this slightly thinned finish on the floor, and work it back and forth (just like glue troweling).
Another method is too simply brush a coat diluted about 10-15% with the thinner that is supplied by the manufacturer. This thinner will speed up the dry time only just a little. But applying a thin coat is the important thing here.
Only VM Naphtha will speed up dry times, and odorless mineral spirits will slow it down. So, in the hot humid summer time you may want to use naphtha, or else the finish will take too long to dry. But in winter, in a warm, overly dry house you might want to use odorless mineral spirits, to slow the drying of this first coat, so that it flows better. I avoid all of this by using the trowel, and apply this first coat of finish THINLY instead of thinned. It’s a skill a pro should learn.
Some manufactures refuse to supply any thinner with their finish. They site the VOC regulations and state in their directions that the finish is NOT to be thinned. Boy is this dumb. If you insist on applying the first coat full strength you will in most cases have a bubbled and pitted and very slow drying finish, but you will be following directions. Good for you. In this case try to get the best paint thinner you can buy, when you wish not to speed up or slow down the dry time like I mentioned earlier. You want in any case, to apply a thin coat, no more that 700-800 square feet per gallon.
AND IN EVERY CASE, NEVER USE A LAMB’S WOOL APPLICATOR. Brush sparingly in any direction to wet the wood, them comb once with the grain. Don’t play around with the finish it will only cause more bubbling. And that is why I always trowel on my first coat, I don’t get any bubbles with this method. A pro should learn to trowel, it saves finish and time.