You start at the consulate of your country.
They will give you a list of the required documents, translated and legalized.
With time you will receive a temporary VISA from your consulate.
Once here you have to make a personal account and page on
www.migracion.gov.do. Scan all the documents in jpg. and
Upload them.
They will revise the documents and after a while you will be invited to go the capital, there you hand all the documents, pay the 14.000 ( in my case they charged me 28.000. Overstay) and the next your medical exam.
Then wait untill everything is ready.