Wet sand 400 grit

Yeah = wet sand! 

How about 600?

I'll see your 600, and raise you - 

800 grit; some folks go 1200 or even more, and then really fine after the last coat is on.

Get a bucket, and keep it wet!

I have a question. How many coats are required to do a really professional varnish job?

At a minimum 3 coats to 5 coats.  The last kayak I built the varnish really flow out great when I wet sanded from 320, 400, and finally 600 for the last coat of varnish.  After you varnish go over the boat in detail to find any runs or scratches due to coarser grit sandpaper.  Once you get to 600 grit these scratches will start to show, if they do show up go back with coarser grit and then go forward and step up the grit of the wet sandpaper..  Cabinet scrapers works great on taking off the runs.  I used Interlux Schooner Varnish thin down with Brush 333.  I thin down about 10%.  Its hard to tell that the finish wasn't a spray on finish on my last kayak build.   Good luck!

You need to be careful about how fine a paper you use between coats.  I use Epiphanes for my builds and on the bright work on my big boat, and they recomend not going past 320, but you can go to 400, as each coat is a mechanical bond, and you need a certain amount of "tooth" to have a good bond. I think that technique plus luck on the final coat is what gives you the sprayed look.

Agree that 320 the finest grit between coats.  I u'se a dry tack cloth I've had for some time.   You just shake it good between uses and when it gets real dirty, toss it in the washer, if you have  permission to use that equipment.  The following is a reference to Norton sbrasives about the cloth. 

http://www.paintpro.net/Articles/PP701/PP701_productnews-Norton.cfm