Do you need a tool to put a freewheel onto the hub?
 

I bought this rear wheel:
http://www.niagaracycle.com/product_...ducts_id=31579

and this freewheel:
http://www.niagaracycle.com/product_...ucts_id=411920

and basically just screwed on the freewheel by hand. I figured if it wasn't tight enough pedaling would tighten it. I tested in out the it feels wobbly and I'm hearing a clicking when I pedal. Do I need to use a freewheel tool to put it on?

Assuming it threaded on easily, there's no chance that you cross threaded it, so it's almost certainly on right. Freewheels self tighten under torque so no tool is needed.

Slight wobble is normal because the freewheel and hub bearings are independent and rarely (if ever) perfectly on a common axis. It's almost impossible to get perfect axial alignment on threaded assemblies (doable, but expensive in production), so that misalignment shows up as the classic freewheel wobble when coasting.

The freewheel should click when coasting, but not when pedaling. If there''s clicking when pedaling look for a cause other than the freewheel because it has no moving parts under load.

You will need a tool to get it off, as the way it freewheels
is the direction that you turn it to take it off.