How to run agar gel electrophoresis at home
There are a few reasons why this is usually not suggested. 


DNA itself is not visible (at least not in the quantities you'd run on your gel). You need a compound (dye) that binds to the DNA to make it visible, and because they bind to DNA most of these compounds are carcinogenic. Even if you use such a dye, many of them only show up under UV light, an additional difficulty. You could also buy a safe dye that works and is visible, but that makes staining also more laborious. Food coloring will be visible all the time, already when running the gel.
The nice CSI gels you see on TV are showing (supposed) PCR products of short tandem repeats, giving you nice bands at different heights on the gel. These bands also have a convenient size for gel electrophoresis. Restriction analysis of plasmids is also something you'd see more often, and also here the pieces are between 100 and 10,000 bp. DNA extracted from plants consists of genomic DNA, huge strands (millions of base pairs) that will not really run on an agarose gel. Getting a selection of discrete-sized DNA fragments is really not so easy in your kitchen, that's why they go for food dyes.