I'm becoming more interested in genetic engineering as I learn more about it, and it's becoming more and more apparent that there's very few resources on genetic engineering at home. A similar question was asked here, but the best answer linked to a failed indiegogo campaign. Is it feasible to genetically modify an organism without a laboratory setting? If so, what materials could be used to do this?
Thought I'd attempt to expand this into an answer, THOUGH THIS IS IN NO WAY MEANT TO SUGGEST YOU SHOULD ACTUALLY TRY THIS. THERE MAY BE LEGAL ISSUES INVOLVED IN CREATING A GENETICALLY MODIFIED ORGANISM, EVEN A HARMLESS ONE, DEPENDING ON YOUR LOCATION. SOME OF THE CHEMICALS REQUIRED TO HANDLE DNA ARE DANGEROUS, AND SHOULD ONLY BE HANDLED IN A FUME HOOD AND WITH PROPER PROTECTIVE EQUIPMENT. I HIGHLY RECOMMEND THAT YOU DO NOT ATTEMPT THIS.
First, you cannot do genetic engineering outside of a lab. You might be able to set up a lab at home, but don't expect to do this using standard household chemicals. Lets assume you're only interested in adding DNA to bacteria, because that's relatively simple.
The first step you need to add DNA to bacteria is to get the DNA. Your major plasmid suppliers probably won't like selling to a non-lab, but if you're lucky you might get some from Invitrogen, Aldevron, or another supplier. If you know someone who works in a molecular biology lab, you might be able to get some from them, but that might violate rules with their university or employer. If possible, I'd get a green or red fluorescent protein gene, as those proteins are easy to detect using a UV lamp you might be able to build with UV LEDs, you might also be able to use a black light. Note that I do not know what promoter would be best to use on your gene. The lac operon is often used to express proteins in BL21 E. coli using the molecule IPTG as an inducer, but that requires you to have IPTG and BL21 bacteria.
Speaking of bacteria, you need competent bacteria. E. coli is the most often used species, but several strains are available. DH5a E. coli is most often used to grow up DNA plasmids, which is something you'll want to do because you probably won't be able to get much plasmid, so you have to make more or you'll run out. But DH5a usually isn't used to produce protein. BL21 E. coli is most often used to produce protein, but you'll probably need IPTG to induce the bacteria to make the protein. You might be able to get IPTG from Sigma Aldrich, but good luck getting them to sell anything to you.
Once you have the bacteria, you'll need to grow them. You need bacterial media, which might be obtainable because it's relatively safe. LB media is a mixture of yeast extract, tryptone, and salt. If you want solid plates you'll need agar too. You can probably get the media sterile enough by boiling it. You'll need some ampicillin or kanamycin to make sure only bacteria with your desired gene is allowed to grow, again Sigma Aldrich might sell it to you.
Of course you can't just put DNA into bacteria, the bacteria must be competent. You can make chemically competent cells by carefully treating them with calcium chloride and magnesium chloride. You'll also need dry ice, these need to be kept very cold. So now you can add your plasmid your competent cells, heat shock them in water at precisely 37°C for precisely 60 seconds, and plate them on your agar media. Then you need to incubate them at 37°C overnight.
If you need to purify the DNA plasmid back from the bacteria, you need to pick a colony off that plate and put it in liquid LB media, also at 37°C overnight with antibiotic. Here you'll need a centrifuge to spin down the cells and remove the left over media. Then you'll need to lyse the cells to release the DNA. You might be able to do this with soap, but you'll probably need NaOH and SDS. Once the cells are lysed you need neutralize them with an acetic acid solution, vinegar might be good enough. Then you have to centrifuge the cell debris to pull the insoluble crap out and leave the plasmid DNA and RNA in the supernatent. At this point you can extract the DNA and RNA with a phenol:chloroform:isoamyl alcohol mix. Good luck getting that, as the vapors from that solution are harmful to inhale, and really bad if you spill it on you, and should not be used outside a hood. But if you manage to get the extraction to work, take the top layer and add an equal amount of isopropyl alcohol and put it in your freezer for a couple hours. Then spin it down, carefully remove the supernatent and you should have a pellet of DNA in the bottom. You might have to clean the pellet with a 70% ethanol solution (140 proof) and another centrifugation. Quantifying your DNA at home will be almost impossible.
Also, this all assumes you just want to put a ready-made plasmid into bacteria. Trying to change the plasmid will require restriction enzymes, PCR, etc.
So yes, you can do genetic engineering at home if your home has an incubator (preferably with shaking), a centrifuge, a water bath, a -80°C freezer, a fume hood, a variety of chemicals, and a decent set of pipettes. But if you have $10,000 you don't really need you might be ok.