Not 100% impossible, but highly unlikely (upwards of 99% impossible) for the average home experimenter to be able to do.
Your biggest barriers will be
Cost - you need extensive, very expensive equipment and lots of it to get these sorts of things to work. You also need lots of reagents, many of which are expensive (roughly in the 100's to 1,000's of dollars for a single attempt), temperature sensitive, and unavailable to the average person (i.e. you need to be working at a registered business or research institute before they will sell them to you; you can't just get these off the shelf somewhere). To equip a lab for equipment alone will be in the \$10,000 - \$50,000 range, depending on what you buy and exactly what you need.
Time - this is not something the average person could pick up a book or watch a video on and do, it takes years of training to a post-graduate level before most people attempt this sort of thing.
Regulation - this is an advanced technique for genetic manipulation; you may not have any malicious intent; but there are environmental laws in most countries that regulate the use of genetic manipulation. If you get caught the penalties will be very high.
Assuming you have enough of 1 and 2, you still won't be able to get around 3.
Having said that - techniques/areas you would need to learn: Plant cell culture, sterile technique, preparation of reagents, molecular biology techniques such as PCR (you have to have some way of determining if it worked...), plant physiology (to make sure that it is something feasible biologically and to be able to work out if something is going wrong, and exactly what that is), plant anatomy (where to source the protoplasts).
Scientific method will also be a big one - you would need meticulous attention to detail, recording everything, so that when something goes wrong (and it will; I'm a research scientist writing this) you might have some idea of what went wrong and maybe why and what to do next. Empirical technique (i.e. trying one set of conditions -> didn't work -> alter single factor in the next one) seems to be the way most people do this , but there is a whole field of literature with several hundred scientific papers on somatic hybridization, and what works for one species might not work for another.