how does anything leave or enter the nucleus
The double membrane, called the nuclear envelope, in eukaryotes, separates cytoplasm from nucleus. The communication and exchange of materials between cytoplasm and nucleus is allowed by nucleus pore complexes, that penetrate nuclear envelope. Nuclear pore complexes build a complex structure, consisting of 30 different nucleoporins.
It is considered that the exchange of nuclear and cytoplasmic contents involves two processes, passive diffusion and active process, both being interfered by nucleus pore complexes. For a while, it was believed that the maximal size of proteins that passes through nucleus pore complexes is of 60 kDaltons, but experiments disapproved this theory, showing thatnuclear pore nuclear pores allow diffusion of proteins having sizes in 90–110 kDa range. It has also been demonstrated that protein interaction with nuclear pore components could help protein diffusion through the nuclear pore.