I am EU citizen (Lithuanian) and my husband is citizen of Dominican Republic. At the moment we live in Dominican Republic, but we want to move back to Europe, preferably to the Nederlands with a purpose of finding a job resetteling. What would my husband need to do in order to get the neccesary permits (work permit and residency)?
Generally speaking, the easiest route/most important thing would be for you, the EU citizen to find a job. Almost any job, even part-time, should do. Alternatively, you would need to establish you have enough money to support your family without seeking financial assistance from the state. See US Citizen with EU Spouse who doesn't yet have a job for a thorough discussion of these principles in a slightly different context.
Once you qualify under those rules, you have to register with the IND (it's not mandatory for EU citizens anymore but you do need to do it to be able to sponsor your husband) and your husband can then apply for a residence “document” (technically not a permit) as family member of an EU citizen (in Dutch: verblijfskaart van een familielid van een burger van de Unie or verblijfsdocument familielid van een gemeenschapsonderdaan). This status would allow him to work without restrictions.
Another difficulty is that since your husband comes from the Dominican Republic, he needs a visa to enter the Netherlands. In principle, he is also entitled to a visa to accompany you but you will need to apply for it in advance. You cannot just show up and sort things out later.
Note that the Dutch tend to be more restrictive than most with the rights of family members and have announced their intention to crack down on EU citizens flouting these rules so it's important to make sure you get the paperwork in order. If you move to the Netherlands, it's also necessary to register with your municipality of residence within a few days (that's unrelated to the visa/permit aspect and also applies to Dutch citizens).
In addition to what Gala said, your husband will need to pass a integration test
Basisexamen inburgering in het buitenland in Dutch before he is allowed to even go join you (https://kdw.ind.nl/KnowledgeRoot.aspx?restart=true&knowledge_id=MWOBasisexamenInburgeringInHetBuitenland&jse=1), while you are in the Netherlands finding work.
After that , once he is in, he gets a 1 year permit (with right to work), then that can be renewedand then after that he might ask for an indefinite one. Additionally, if he lives 3 years in the Netherlands as your husband he has a right to nationality (what i did). Also he has 3 years to pass another
inburgering exam to prove his desire to integrate under penalty of being having his permit revoked.
Source: I came to The Netherlands under the same conditions in 2010. (i'm finally a citizen)