my son has been working since april and has made over 5800 but has not paid for his own support. do i claim him as a dependent and he files his taxes separately or do i add him to my taxes?

“my son has been working since april and has made over 5800 but has not paid for his own support. do i claim him as a dependent “---->It depends on the situation; as long as your son is younger than 19, or a full-time student younger than 24, or permanently disabled at any age, and the child must live with you for at least half the year, and you must provide at least half of that child's financial support.Then regardless of your son’s gross income, you can claim your son as your dependent as a qualifying child. If NOT(for example, if he is 19 yo or a full time student 24yo), then, you can’t claim your son as your dependent.
“and he files his taxes separately or do i add him to my taxes?”---->As long as he is married, dependency can be claimed for a married child if the child does not file a joint return with his spouse. (Spouse must file as Married Filing Separate.) The child has to meet all the other requirements for dependency, including income less than $3,650 for 2011, and you have to provide more than half the support. The child, regardless of his age, would then fall under the qualifying relative guidelines, rather than qualifying child. If the son is NOT your dependent and file his return, then you can’t claim him as your dependent. OR as long as your son under 18 who earn less than $9,000, according to IRS 2011 tax rates, may include income on your tax return. Then your son doesn’t have to file his return. You must gather all the earnings, interest and capital gains from employment, savings accounts and investment accounts to determine if the aggregate value is less than this threshold.

So he is under 19 and his gross income is under 9000. He doesn't have to file and I can claim him as a dependent?

yes you can.