Blanchard:
First, I am a little confused. Are you currently an employee or a contractor? The tax situation is different for both.
If you are an employee. . .
1. There is a formula on the back of a W-4 form (the one you fill out when you tell them how many exemptions you want). This VERY long and confusing process will fairly accurately tell you how many exemptions you would be best to take. Or you could just guestimate. If you are married and your partner makes much less or much more than you do, you should claim at a higher single rate and with less exemptions than you actually have. This will have more taxes withheld from your pay check. If you are unmarried without dependants I would almost always claim single and zero exemtions. If you also have some other type of income you can always have your employer withhold an extra amount with each check.
2. Yes, you can pay your taxes as often as you like. Just be forewarned that once you start what is called estimated taxes, the IRS doesn't like it a whole lot when you stop. If you end up oweing a large amount at the end of the year you should either be withholding more on your paychecks or you should be paying estimated taxes. The IRS can (and will) charge you penalties and interset for failure to pay if 90% of your owed taxes are not paid quarterly. This means that if you are owing more than you had withheld for the year then they can come back and charge you for it.
To get set up on estimated taxes you can go to
http://www.irs.gov or I believe there are forms at your local library. I would highly recommend this.
(part 2)
If you are a contractor:
1. On your I-9 form (the form you fill out with your SS# and address) you have the option of having your contractee withhold 15% of your pay for taxes. If you are ending up with a large amount due at the end of the year this might be an option for you.
2.See above #2. Also, as a contractor you will be responsible for Self employment tax if you earn more than $600 in a calander year as a contractor. That is where the expense of being a contractor lies. (That is also the calculated 15% from #1)
Good luck. Sorry for the long response.