A few months back we were traveling to India on Emirates airlines and decided to spend a week in Dubai when returning back to the US.
Indian passport holders with US green card need a visa to enter Dubai. If you are ticketed on Emirates airlines, then the airlines can sponsor the visa. The visa can be obtained from the CIBT emirates site http://legacyus.cibt.com/DVA.aspx. A 30 day visa will cost around 73US$ at the time of posting this entry. Application process is straightforward, scanned copies of passports are required.
The visa will be an email, which you need to carry at the time of entering Dubai.
The immigration formalities were as follows :-
1) We had to go to a section with the board visa collection, there was separate section called Passport control, but Indian citizens had to go to the visa collection section first, here the immigration authorities will see your email printout and do an iris scan and stamp the entry date on your email printout.
2) Once step 1) was done, we had to go to the passport control line, where the authorities stamped the entry date on the passport.
Currency is Dirhams, which you can exchange in counters within the airport.
Formalities when exiting Dubai :-
1) The exit date was stamped on the passport.