The main way the immune cells recognise foreign things inside a cell is by detecting them outside the cell. Part of a cell's natural processes is to breakdown some components that are inside the cell and 'present' them on the outside of the cell. These are called antigens, or peptides.

If they are 'self' peptides, then the immune system has been trained to recognise these as safe and so it doesn't react to them.

If they are 'foreign' peptides, then the immune system recognises them, and subsequently targets that cell for destruction - either by releasing chemicals that perforate the cell membrane, or by recruiting other cells to do the job.

You can get some treatments, such as antibodies, which can have a chemical drug attached (ADC - antibody-drug conjugate). The antibody targets a specific cell type and then when it gets there, it releases the drug, which goes into the cell and targets a disease, or kills the cell itself.

There are other methods, some described in other answers that work in different ways but have similar aims of targeting something inside the cell.

When things go wrong with this: The immune system incorrectly recognises self peptide as foreign and attacks healthy cells (autoimmune disease) The immune system does not recognize foreign peptide correctly The disease stops the infected cell from presenting the foreign peptide on the cell surface - avoiding detection The disease hijacks the presentation process and gets the cell to present a self peptide that would normally not be presented suppressing the immune response that would normally happen.