I have read the discussions regarding high gloss finishes, but haven't quite found the answer I'm seeking for my unique situation. I have a built-in cabinet in my condo. It has dark stain and varnish. I would like to give it a glossy, black finish. It doesn't have to shine like a Steinway, but I would like to completely cover the wood grain. Because it is a built-in and in my living room, spraying is not an option. Nor is any wet-sanding/polishing. I would also prefer to avoid stripping the varnish, if possible. Is there a way for a novice like me to achieve the finish I desire within all of these constraints?
It's easy enough to get a glossy finish (see Graphus's answer), the hard part is getting it flat.
With a gloss finish any surface imperfections become very easy to see. This includes the grain of the wood (particularly if it's an open-pore species like Oak), dust that may settle on it before the finish is cured, orange peel from applying too much or too little finish (particularly if spraying), brush strokes, previous surface imperfections, etc.
This is the reason that people often use a regime that involves finishing in thin coats and sanding repeatedly. If you just want it to be shiny then any gloss finish should do. Oil-based paints are a little easier since they self-level better and tend not to leave brush strokes, but the clean-up is more annoying since you need to use mineral spirits instead of water.
Paint it with gloss enamel.
Use a small brush or 'detail' brush for inside corners and tidying up edges, a foam roller for the flat surfaces.
You'll need to scuff up or lightly sand the entire piece before you start to ensure good adhesion so some dust will be generated but not an excessive amount.
Finishing is under most circumstances, messy and there really isn't a way around this. No matter how careful you are, there will be drips, runs, splatter, etc.
You've already mentioned a few possible constraints like not spraying and finishing indoors. Let me address the latter first. The typical concern indoors is VOC's and explosion hazards. Because of this, I would recommend a waterborne (water based) finish. There are some good quality, WB lacquers that can be brushed or sprayed. One I've worked with is Target Coatings Emtech EM6600 (no affiliation to them just a good product IMO).
A common reason people don't want to spray is that it is messy to due overspray. I would suggest that regardless of what method you chose, you are going to need to mask off and cover parts of the room. Covering everything in plastic drop sheets taping them down is a bit of work but at the end of the day is not all that difficult and will ensure everything near by stays perfectly clean. Once you have this in place, spraying might be a viable option, or you might consider a hybrid approach (brush and sprayer) for different areas.
As far as refinishing the cabinet, you are going to need to sand it no matter what method you use. You should then put down a sealer coat - shellac is a good universal sealer and you can even find WB-based variants (see the site I linked to previously). From here you will apply a pigmented coat - could be lacquer, latex-based paint, etc. Optionally you can put on a top clear coat if the finish of the pigmented layer doesn't meet your required level of shine.
A couple steps I would suggest.
1) Apply a deglosser. Products like this soften the surface to allow for better adhesion to the substrate.
2) Apply a heavy duty primer (it will smell) I suggest BIN's red labeled alcohol based primer. This will seal in the stain and even out the surface for painting.
3) Let the primer cure. Follow the label
4) Apply a black gloss finish of your choice. I'd suggest a gloss black lacquer if you really want that super shiny finish.