The company usually submits your papers to the Residence and Borders Department of the Ministry of Interior.
As for you, attend the clinic in Wasfit Tal St (also called Gardens St) for your blood test. It's the one where all foreigners go. You collect the results about a week later. About two years ago, the cost was 30 JD.
Submit your blood test results and passport to your company. They will do the rest.
Upon approval, you shall receive a residence permit (iqaama) and a work permit.