The end goal of GMing an organisms is getting new DNA into the organisms germ-line cells (i.e. sperm/eggs/pollen etc.). For some organisms this is absurdly easy, and simply involves growing the organisms in the presence of the DNA. Most organisms, however, are much more protective of their cells and resist assimilation of environmental DNA (either by degrading the DNA or triggering cell death in cells which assimilate the DNA).
Two main techniques exist for getting foreign DNA into plant cells. The most general technique is to simply shot the DNA into cells attached to tiny inert particles. Once inside the cell the DNA can sometimes stably integrate into the plants genome as a plasmid. I'm not sure about plants, but in animals extra-chromosomal DNA tends to be silenced, presumably to protect the cells from DNA viruses. Therefore if you want really good and stable production of a new gene product, you have to actually integrate the DNA into the chromosomes of the organisms. This requires that enzymes cut the host DNA and the plasmid, and then integration factors splice the plasmid into the chromosomal DNA. Unfortunately the enzymes which can accomplish this feat tend to be specific to closely related organisms, and if you wish to make good GMOs of new species, you have to set about discovering the appropriate enzymes.
There are a host of other little details I could get into, but I think I will leave off at that for now.