LOCATION, LOCATION...
You need to do your homework on where to live. Like any city with millions of people, commuting can be problematic if you get a  home in the wrong city district. So, if you work in Sharjah, consider Festival City; if you work in Abu Dhabi but can't afford their rents, consider Jebel Ali area. Khaleej Times puts out a monthly rental monitor.

Another issue is, if you have school-age children, they will need to be educated at a private school - so first check out the extent of their bus pickup area before you settle on a place to live. Note also that school starts early in the morning and is over by early afternoon, so kids are on the bus around sunrise. 

TYPES OF HOUSING
Many expatriates first look for a villa, i.e. a one or two-story home with its own yard space. In urban areas, these often have high walls on all four sides, with a small yard area. Some of the best villa arrangements share one city block, in a compound with a wall that encloses villas around a common courtyard, outdoor pool and fitness room. Suburban developments have been built on the outskirts of Dubai which are more like the townhome developments in western countries.

More common is apartment or condo living, given restrictions on home purchase. With the innovative architecture that has been given a free rein here in Dubai, these choices range from high-rise aluminum and glass to Arabian-style designs.

LEASE AGREEMENTS
Typically for a year, with four pre-dated signed cheques, plus a security deposit. The first cheque is immediate i.e. three months up front! Some landlords want to get two cheques, or only one (i.e. year up front) but may back off if they realise you can easily lease elsewhere: there is currently a big oversupply in Dubai with tens of thousands of new units coming on to the market. Abu Dhabi is still tight.