I don't thin out a quart at a time.  Pour only enough to do the job at hand into a small roller pan.  A quarter of a can is more than enough to do a boat deck or half a hull.  Thin the varnish with generic thinner (that says it's for paints and varnish) to a consistency just thicker than water (about 1/3rd thinner).  Blend gently (stir, not shake).  Once I'm happy with that, Starting at the bow or stern, I roll it on only a foot, or so, at a time, with a Ultra Foam Smooth Surface 4"foam roller (available at Home Depot) then go over the just rolled area with a 3" wide foam brush, one pass usually does it, then on to the next foot and tip it out again.  The foot sections overlap and so does my tipping out with the foam brush.  Important thing here is not to rework or overwork any section.  I use a good light source reflecting off the wet varnish in order to see any holidays as I work along the boat. 

 Hope that's of some help and I'm sure there are many, many other ideas out there, but the above works perfect for me and, as that lady on TV says, "It's a good thing".    

Forgot two things.  Thought of them while walking the dog.  1) start brushing your first rolled foot with a semi-wet brush.  That will keep the brush from soaking up too much varnish which would result in a rough looking first foot.  Don't dip the brush in varnish from that point on.  2)  Always brush in the same direction from well into the dry to well into the wet with overlapping,a continuous long (two-three foot) stokes.  Starting the stroke in the dry allows the bush to shed some of it's excess varnish and avoids runs and sags.  Good luck. 

Thanks Jerry.

I put on a coat of varnish today, thinned as you describe. A very big difference, for the better, for physically working with it, seeing what I am doing as I work and also a nicer finish afterwards. If I had thinned from the first coat, I would be done by now. One more coat tomorrow and I will be finally finished with the deck, then will flip the boat over and put a couple more coats on the hull during the week after work. Then reinstall deck rigging and back to paddling on the weekend! 

From now on I will thin the varnish, always.

Unless it's freezing cold I often find that heating the varnish has the same result as thinning it out and gives a better finnish when cured.  I put the can, with the lid cracked open, in a pan of hot [but not boiling] water for about 5 - 10 minutes before use, and then apply it as suggested by Jerry.  Goes on silky smooth and sets up quite quickly, as long as it's not applied to thick.

Have fun!

 Spring, with all the pollen   and new bugs, and   road dust and gentle breezes   is   a very  difficult time to  varnish,  ( as opposed to  a still warm summer evening ).

  I  varnish in my carport,  completely  tarped with floor to ceiling drop cloths,  and   a gentle misting spray in the  enclosed area  about 2 hours before moving the the boat inside.  Not perfect, but better than in the clear outside, and better than in   a dusty shop.