Unless someone has been modifying that engine, odds are in favor of them being hydraulic. To tell, pop a lifter out and take a look. A hydraulic lifter will have an adjustable plunger with a snap ring, and holes for oil to enter and exit. A solid lifter by definition, does not have this mechanism.
Solid lifters are typically only used on performance motors where their better valvetrain control at high lift/high rpms outweighs the need to periodically adjust them.
Hydraulic lifters are self adjusting, and set up based on preload. Methods vary, and some disagree on just how much preload, but since they are self-adjusting, there is some wiggle room. The way I was taught is when the valves are bottomed out, tighten the adjusting nut while turning the pushrod until it starts to drag, and then one-half turn after that, then rotate the engine and set the other valves. An alternative method is while the engine is running, and tighten the nut one-half turn after the ticking stops. Typically messier, but it works. Like I said, everyone's got a method.
Solid lifters are set up based on valve lash, which is the amount of clearance between the cam lobe and the valve stem. This is done using a feeler gauge. These have to be adjusted periodically. On what sounds like a relatively stock 350, it's doubtful this is what you have