Hi, there are a couple steps you can follow to do this successfully:
1. Decide which primers you want to use such as the CDC N-gene primers:
use only the forward/reverse primers, not probes. Other countries like Japan, China, etc. have different primers as well
2. Test your protocols using synthesized DNA (bacterial plasmids) matching the SARS-Cov-2 gene you are looking at
See here (bottom of page under plasmid controls)
If your assay works you should run the PCR on the plasmid DNA + primers and should get a gel band that you can size with a DNA ladder (you'll need a small range DNA ladder size like 25 bp or so since the amplified viral fragments are really short). You have to be careful though because the amplified fragments are so short, spurious PCR results like primer dimers can give bands on gel that are spurious false positives.
3. Now if all these works successfully, to amplify a real sample, you need to be able to 1) isolate the RNA from a sample and 2) get a kit that converts RNA to DNA that can be amplified in PCR.
For #1 there are viral RNA extraction kits you can buy, but the bad news is most require a centrifuge that forces the sample (i.e. treated mucus) through a filter at high g. I can find some links if you want.
For #2 There are several ways to do this. They all involve reverse transcriptase (RT) enzyme though. Some have kits with "random hexamers" which is a fancy way of saying there is a lot of random 6 bp DNA that RT uses to make the DNA from viral RNA. You have to use these kits to make the DNA (not too hard honestly) and then amplify that in PCR. OR there are master mixes out there that have RT in them as an ingredient and do both the RNA->DNA conversion as well as amplification in a specific set of thermocycler runs. The latter are much easier but less flexible as far as if you have to tweak the mix to get the amplification to work.
That's basically the gist of it. I personally am biased toward getting Sanger sequencing done (it is super cheap, like $6 per sequence). But the gel method can work too.