No apologies necessary - I just couldn't resist 
My clarification was not only for you, but also for others that continue to ask about the database - not that everybody now rephrases their questions to ask for the API to change the database
This question is a lot easier to answer (though, admitted, the naming is a bit of a mess)
The API methods for users and usergroups are in UserService, UserGroupService, or the equivalent local services. UserLocalService does not check any permissions, but for example you might want to look at UserLocalService.hasUserGroupUser.
The mess starts when you're getting to all the uses of "group" in that API: "Group" in the API is the technical name for a "Site" (simplified, but you'll get the point), so that "xxxxUserGroupXxxxx" might refer to a mapping of Users to Groups or the UserGroup. And even though I'm linking to the javadoc site, currently it's not the best documented class...
Another option, that would be more advanced and give you more flexibility: You might want to implement permissions - these can be granted per site, through roles. Roles might be assigned to individual users, usergroups or organizations. Ultimate flexibility and you'd use Liferay's permissionChecker to check if a certain permission is granted in the desired scope - through whatever means and memberships.
My clarification was not only for you, but also for others that continue to ask about the database - not that everybody now rephrases their questions to ask for the API to change the database
Angelo Costa:
Rephrasing my initial request what i needed is to understand if a certain user belongs to a certain user group and if so the enable some buttons in the frontend.
For example: I have a user group called "workers" and added a user to this user group. How can i know if the current logged user belongs to this user group?
This question is a lot easier to answer (though, admitted, the naming is a bit of a mess)
The API methods for users and usergroups are in UserService, UserGroupService, or the equivalent local services. UserLocalService does not check any permissions, but for example you might want to look at UserLocalService.hasUserGroupUser.
The mess starts when you're getting to all the uses of "group" in that API: "Group" in the API is the technical name for a "Site" (simplified, but you'll get the point), so that "xxxxUserGroupXxxxx" might refer to a mapping of Users to Groups or the UserGroup. And even though I'm linking to the javadoc site, currently it's not the best documented class...
Another option, that would be more advanced and give you more flexibility: You might want to implement permissions - these can be granted per site, through roles. Roles might be assigned to individual users, usergroups or organizations. Ultimate flexibility and you'd use Liferay's permissionChecker to check if a certain permission is granted in the desired scope - through whatever means and memberships.