Small scale TTL (5 volt logic).

Breadboard with 5 volt power supply. Get the Logic HIGH inputs from 5 volt power supply through a 1 Kohm resistor.

Test the outputs using different inputs according to the truth tables.

That will work for the gates and inverters. Flip-flops and counters are more difficult because you also need a clock signal.

Use something like one of these:
http://www.jameco.com/webapp/wcs/stores/servlet/StoreCatalogDrillDownView?langId=-1&storeId=10001&catalogId=10001&search_type=jamecoall&freeText=breadboard

Exactly what are you doing?