Expatriates will normally enter on a single entry visa (employment visa) valid for one to three months. This will be arranged by the employer. Police clearance (“Certificate of good conduct”) from your country may be required prior to entry - check this first with your employer. If you do need one you can find details here: Police Clearance Certificates for Qatar. Once in the country expatriates will need residents permits and work visas, normally arranged by their companies.
In order to get this, expatriates will need a health check, which will include a blood test and chest x-ray. This will be followed by fingerprinting. You must also get your blood type tested. This can be done at Doha Clinic in Al Mirquab Al Jadeed street for a nominal fee.
Medical checkup - residents of some countries, including Oman and Saudi Arabia, must have checkups before coming to Qatar. This may be extended to a number of other Asian, African and Middle east countries.
Note that, according to the Doha Airport website, sponorship can only be tranferred after an employee has worked for their original sponsor for a minimum two years, although rules like this can be applied somewhat haphazardly. An sponsor can also block his employee from returning to Qatar for a further two years.