The strategy is going to be somewhat virus-specific.

As one user noted, retroviruses go dormant by integrating into your own genome, at which point it becomes nearly impossible to rid them completely. External stimuli causes your own cells to express the integrated viral genome, leading to production of new virus. HIV is going to be the most common example in humans.

Other viruses, like herpes, infect so-called immunoprivileged cells that are considered too vital to be damaged in an immune response. In the case of herpes, nerve cells become infected where the virus can lay dormant more easily, as nerves are immunoprivileged cells. Some viruses, like Zika and Ebola can infect the testes which are also privileged sites.

Another general strategy is for the virus to simply hang out in the nucleus of a cell and stop replicating. The nucleus is a nice place for a virus to hang out because (to my knowledge) there aren’t really any proteins involved in recognition of pathogens there. Such proteins are typically in the cytoplasm, within endosomes, or on the cell surface. Furthermore, if a virus stops replicating then there’s not much material for our immune system to recognize. That I know of offhand, herpes, HPV, and cytomegalovirus (and probably MANY others) all employ this strategy.

Most viruses that go latent also express proteins or RNAs that inhibit our body’s ability to recognize pathogens. These come in many different forms but as an example HPV expresses E6 and E7 proteins which cause the infected cell to express fewer genes involved in viral clearance. Another example is how ebolavirus VP35 protein blocks the RIG-I receptor (which recognizes viral RNA)

Last mechanism that comes to mind is that some viruses simply infect areas that aren’t easily accessible by our immune system. HPV infects the epithelia of the uterus in a particular region that has very high cell-turnover rate. Because epithelial cells are constantly being shed in this region, immune cells can’t really patrol it very efficiently.

Anyways I’m just going off memory with this response so sorry it’s all over the place. Hopefully there’s something useful.