Is it possible to genetically modify a plant at home?
Well, that depends on your home. ;) I think it is not an easy process.

There are two main methods that are used to genetically modify plants:

Using the bacterium, Agrobacterium tumifaciens, as a vector for the DNA. Agrobacterium has the ability to infect plants and insert DNA into a plant's genome. It causes crown gall tumours in natural infections. This method has mainly been used to modify broad leaved plants, such as sugar beet and oilseed rape, but is now also being applied to monocot species, such as maize and rice

Particle bombardment or biolistics where the DNA to be inserted is coated on minute gold particles and fired into plants cells. This approach is used for monocot plants such as maize and rice

Here I found simple step by step article, but lil bit old. may be there are new methods for this process.
How To Genetically Modify a Seed, Step By Step