Some counties now have certain of their records accessable online, including documents in the RODs office. You can do your own searching in such counties and then print out your result on your home PC. Most will, however, charge a small access fee based upon usage.
Vital records will NOT generally be available to the general public, unless quite old (for geneoplogical research purposes). This is to protect against ideentity theft and misuse. So the party requesting the record must either be the party, or a relative who would have a right to such a record. I CANNOT write and obtain YOUR birth or marriage record, for example, but I could obtain my daughter's or my Grandmother's.