Residency is tied to the Emirate where your employer is, not emirate you live in. So if you live in Dubai but work in Sharjah (or vice-versa) carefully check website of their Department of Naturalization & Residency.

You can't make a contract over 30 days until you get residency, so you may be in a hotel without ability to sign a housing lease. Get all necessary attested document originals to your company HR dept ASAP, plus have them schedule your government medical certificate (no TB, no AIDS).

Getting your Residency visa is your employer's responsibility: see Residency link on the Mobilization webpage details. Getting spouse's visa is your responsibility as their sponsor - check out DNRD and SNRD websites.