Open Question: How can I find out what my payroll taxes are?

i just started working a taxable job after working under the table for a long time. i want to know how to interpret the taxes that are taken out and how they decide how much to take out. is there a table of some kind that i can look up on the internet? my employer is in new mexico, though i occasionally work out of state. my first check was for a day and a half and the taxes that were taken out were about 9% of my earnings. the second check was for a full two weeks and about 23% was taken out. this one of the main things i want to know about.