An online copy of an RCA tube manual (as mentioned by Viridian) that talks about the general measurements that determine how a tube performs. RCA Manual
The discussion about tube characteristics starts at page 10. Tube curves and load lines are about the most useful general info you can get about tubes and tube circuits.
There is also a discussion of how to use plate curves and tube load lines here. This is a classic article by Norman Crowhurst.
A short description of what a tube tester does is below. It gives you specific info about the tubes in hand that cannot be obtained from general info above. Rozenblit's site
If you want to buy a book Bruce Rozenblits book Beginners Guide to Tube Circuit Design describes all of this very well and is only about $25.
Cheers,