Stiggy baby and Jersey Guy, the information posted by Gringo carlos is basically what you need to know. I dont know why this consulate worker named Michael gave you such an upbeat assessment of the situation, because frankly, even according to the consulate's list of requirements, it is obvious that the application will not be easy. YOu have to show that you own property (not just some little house worth a few hundred thousand pesos, but real property); a bank account (not only to show how much money, because as Gringo Carlos points out they are on to that scam -- it is just to show that you are rooted here, that you have lots of reasons to keep you here and guarantee that you wont overstay your welcome in the States).; a good job; -- and anything else that demonstrates this rootedness in the community. The medical insurance is a nice touch.
Normally all this arranged through Banco Popular. You go to a branch, fill out an application form (forget how muchthey are charging but it aint cheap), and you are given an appointment -- which might take place as much as three months later. Yes, the lines are long. you show up like the rest, at dawn, wait on line, with all your paperwork, and hope that the interview goes well.
Now that is about all you can do if a friend or girlfriend is the one doing the application. If you are here, you might go along to the interview in order to assure the consulate officer that there is no reason to worry about abusing the tourist visa, and you can act as a kind of guarantor (though in fact, your presence is not at all a real guarantee, but the support might tip the balance).
Bear in mind that the process has gotten tougher in recent years, so as one consulate worker told me, there is no guarantee whatsoever, even with all the proper paperwork, that the person will be given a tourist visa -- even if the person is amiddle class or upper class Dominican -- they too have abused this privilege and overstayed their visas.
I cannot give you odds on the likelihood that a visa de paseo will be granted. But if you really care about these people and want them to visit, by all means give it a shot. The process doesnt really cost all that much, and the Dominican might just succeed in getting the visa.