Here is a list of the minimum stuff you would need. I prefer a better digital scale or balance type made by Ohaus/RCBS like the 5-0-5 over the Lee scale (yes the Lee scale will work) There are hand held presses made, but they are only a few dollars cheaper and much harder to hold onto when learning to prime and add powder. Bench style is easier for most uses.
Lee 50th Ann. Kit 90050 $104.49
Lee .308 Win RGB FL dies 90879 $13.48
Lee .308 Win case length gauge (to trim) 90139 $.3.99
Lee #2 Shellholder (used on 308 among other cals) 90519 $3
Lee Manual 2nd Ed. 90277 $17.98
Pair of digital calipres from Home Depot or CT $30
1/4" bolts/nuts washers to hold press down $5
Table or bench to attach press to, or a board and clamps to hold the board on table $?
Safety Glasses and a notebook to record what you made in
If you bought the RCBS Rockchucker Supreme kit it has a manual, but you still need a case trimmer, bolts, table, calipres.
With any kit you will need .308 brass, large rifle primers, 147-173gr .308" bullets and a suitable powder for that rifle like Win 748, IMR 4895, H-4895 or IMR 4064.