My husbands employer does not take out any taxes, fica, medicare, state, federal, of his payroll checks, is this right for him to not do this? And does that mean, my husband has to save up from every paycheck and file whatever at the end of the tax year? I don't even know what to file or percentage to keep... how do I find that out?

It depends on his actual status ... is your husband considered a 1099 Comtractor? IF so its his responsibility....It doesn't sound like he's an employee, but a contractor to the person writing the checks.

If he's actually an employee....(yes it does matter) then his employer should be takign out the taxes. As you can see there isn't a one size fits all answer.

If he is you don't even wait until the end of the year... you have to do it quarterly. And the percentages and ammounts woudl be based on what Country he lives, what state he lives, and in some cases what COUNTY and City he lives as some have their own payrol taxes.

The first year of self employment doesn't require quarterly filing.
He should be saving about 25% (depending on the amount, your deductions, etc.)
He should be saving every receipt for every little purchase and expense that might be remotely related to the job.
He should talk to a tax adviser now.

It's possible that his employer is doing this illegally. If you want to ask about that by telling us what he does, whose equipment he uses, and whether he has other jobs, it will be anonymous here. Some employers do this to save money and take the risk of getting caught by the IRS (VERY costly mistake). If your husband is being paid incorrectly, the employer has to pay the back taxes. If not, or he never gets caught and your husband doesn't want to lose the job by turning him in, then your husband has to pay self employment tax plus personal taxes for the two of you.
A self employed person doing the same job as a wage/salary person should charge about 30% more, depending on various factors.

Both Smoothy and Joy have given good advice.