Upvote:2
The details depends on the country.
Some countries have no rule at all, some have intergrated it into their own, national, registration laws.
In Germany, everyone must register their residence when moving in to a new address. When a EU citizen does this the first time, this 3 months condition is considered to be fulfilled. Nothing more needs to be done.
Without knowing which country you are presently are living in, no usefull information can be given other that border hopping is not a solution.
Upvote:2
When can I go back and keep living in that country after leaving when my 90 days is done?
There is no strict 90-day limit, nor a strict 3-month limit. There is a right to reside for up to three months with almost no conditions and a right to reside for more than three months that is subject to somewhat greater conditions.
This means that a country can impose penalities for exceeding three months without meeting the greater conditions, but there is no requirement to impose any penalities. Thus, the existence of any such penalities depends on which country you're in. It could also depend on your circumstances.
In general, if you have the means to support yourself, you can stay as long as you want, and if you fail to comply with any registration requirement imposed by the country where you're staying, you can be fined. Whatever penalty is imposed must be "proportional" and cannot include expulsion simply for failing to register.
Whether a temporary absence from the country would reset the three-month clock would likely depend on circumstances. If you have a fixed place of residence, most legal decision makers would probably find that a short trip out of the country does not interrupt your residence. If you're traveling around from place to place, a short trip abroad is more likely to help, but it's far from guaranteed.