I use a conventional (pre-TN) start, so I only get one yard. Now that Steve's added the 'Continual Capacity Increase' option I turn that on right away, and my yard ends up 10,000 to 12,000 tons by the time I get around to building a second one.
The very first ship I design (and build) is a basic Geo survey vessel - one or two engines, geo sensor, fuel, armour. I keep it small enough to stay under the Maintenance Facilities limit (1000 tons unless I've built more) and send it to survey my home system. In the mean time, I research & design a larger combined Grav/Geo Survey vessel with a jump engine and retool the yard for that. Once I have enough* explorers, I retool for a couple of warships (in the aforementioned 10,000 to 12,000 tons range) and build a second yard for my explorers. I also build a commercial yard** tooled for my colony ships, and therefore able to build my freighters as well. Later a second commercial yard for my eventual terraformers, asteroid miners, and troop transports (which all use the same template, with only the 'modules' switched, and thus can all be built in the same yard). Eventually a third naval yard for 'frigates' while upgrading my main yard for 'battleships'.
One thing to keep in mind is that I favour more general ship designs, and far fewer (if any) retooling between disparate classes than other players. My frigate & battleship yards are almost always retooling for a new class, but it's a new class of 'frigate' or 'battleship' with a very similar design philosophy. I don't do the 'four missiles cruisers, then four PD destroyers, then four beam cruisers, then twelve improved missile cruisers, then four assault transports, then four . . .' approach taken by many others.
*What constitutes 'enough' varies from game to game.
**With the latest editions, conventional starts get an initial commercial yard as well.