How do you make a phone call from a US phone to a phone in Dominican Republic?

Mobile numbers in the Dominican Republic are not easily distinguishable from landline numbers. They all use the same geographic area codes, +1 809, +1 829, and +1 849. The country code +1 is North America, the same as the USA and Canada, but area codes 809, 829, and 849 are exclusively for the Dominican Republic.

From any GSM mobile phone, just program in the number as +1 8x9 xxx xxxx (including the plus symbol).

(The plus sign means "insert your international access prefix here." From a GSM mobile phone, you can enter the number in full international format, starting with the plus sign. The most common prefix is 00, but North America (USA, Canada, etc.) uses 011, Japan uses 010, Australia uses 0011, and many other countries use different prefixes.)