Gel electrophoresis is basically a slab of gel usually made of agarose or polyacrylamide and is set into a tank with a pH buffer. You then apply an electric field to the tank that makes the molecules separate, the molecules then move from a negative charge along the electric field to the positive end of the tank. This process is used to separate proteins and others.
Gene splicing is a post-transcriptional modification that can be used for a single gene to code multiple proteins. Gene splicing is only done in eukaryotic cells, and happens before the mRNA translation. It is very important for a wide range of diversity between proteins.
Transgenic Organisms can be used to genetically modify ones genes to either new genes or modify the genes you already have. What has greatly impacted on the help of making this possible is recombinant DNA. Transgenic organisms are also used in our crops to create food crops like these are known as GMO or genetically modified organisms.
http://biology.kenyon.edu/courses/biol114/Chap08/Chapter_08a.html#cloning
http://knowgenetics.org/transgenic-organisms/
http://knowgenetics.org/transgenic-organisms/