Think of transplantation as simply another foreign antigen, like a pathogen. It might be helpful to think of the cells as being 'virally infected' because they're expressing markers recognised as foreign after the transplant, just like a virally infected cell. The cells will play the same roles: helper cells will recognise antigen and secrete chemokines and cytokines to attract other effector cells to the transplanted tissue and help cells like T cells and B cells execute their effector functions. Cytotoxic T cells will directly attack the transplanted tissue by recognising foreign MHCI:peptide complexes on the cells and then secreting granzyme/perforin to kill the cell.
Natural killer cells are slightly more complex in this case and I'm not going to go into detail and explain to you how they're involved because you won't really learn the mechanics of that until third year of university! Literally.
Basically, the NK cells recognise the level of MHC expression on the cell, there are different kinds of MHC alleles just like there are different blood type alleles (A, B, O). Different people have different combinations of MHC alleles and therefore different MHC molecules on the surfaces of their self tissue. If the transplanted tissue /doesn't/ express an allele normally found on host tissue this can be recognised by NK cells as a 'downregulation' of the MHC they like to check for on cells (different NK cells can check for different MHC alleles) and that can 'activate' the NK cell so that it attacks the cell that has failed to express the self MHC. It's kind of like the NK cell thinks the transplant tissue looks like it's infected with a virus, as I said above.
So you could think of it as being like, T cells recognise the presence of MHC that shouldn't be there whilst NK cells recognise the absence of MHC that should be there.
Aaaand I feel like I've probably entirely confused you so I'll end by saying you don't need to know all that detail! Keep it basic - T cells do the same job they would if they saw a pathogen and so do NK cells. It's the CTL and NK cells that will be involved in direct killing of the target tissue because they express 'different' MHC to the recipient phenotype. The T helpers do exactly that - help the other cells along by producing more indirect factors, bring about some inflammation indirectly and etc. I feel like that should be enough detail, but if anyone else thinks differently feel free to add?