There are (at least) two different types of stains for concrete. One is a surface coating, the other is acid etching.
The former can work, but isn't as durable/lasting. I believe most of the products you get at the big-box stores are more of a top-coat type of stain.
Acid etching is just that, it's a stain containing an acid that actually etches the concrete. This is the typical type of stain you see in home magazines and such. The etching provides a deeper stain that is more durable and not prone to flaking.
I've done the latter, and applying it is super-easy. It's the prep work that can be a chore--namely if you have adhesive on the concrete already. In our case, we has tile mastic, which we had to dissolve using soybean based stripper. It worked great but was incredibly messy.
If you don't have glue to deal with, however, you should be good to go. Order up the stain (lots of places online to get it). You then dilute it per instructions and spray it on the concrete. I used a garden sprayer for this. You then let it sit for a period of time, and then you apply a neutralizer to stop the reaction.
After that, you apply water and mop/squeegee/wet-vac it up.
Then, you apply a sealer of some sorts. Common options are wax-based, polyurethane, and epoxy. I went with poly as it was relatively easy to apply (roll it on). That said, I don't think it was ever truly waterproof. For your needs, you may want to go the epoxy route.
Isherwood's statement is correct in that basement floors are smooth but the surface is made smooth using a power trowel. A power trowel would be much too large to use for your application.
I suggest using an aggregate free Portland cement and sand (or silica powder if its available). The ratio is typically 1 part cement to 3 parts sand and water of course. The trick to getting a smooth final surface starts after its poured and before it sets. You will need to create or purchase a float that will be used to produce the smooth finish. After you've poured your mix into the mold, level it out and make sure no air pockets are below the surface.
Within a few minutes the setting process begins. This is when you will see a layer of water develop on the surface. Using your float, skim the surface in one direction until the desired smoothness is achieved. It's that simple!
Also, I suggest reinforcing your tabletop with steel. Chicken wire (as it's called around here) should work well or some other mesh type steel. Good luck and post some photos of your final creation!
Best Answer
All sealers that I have worked with require a clean, dry, scale free, dust free surface. A vacuum cleaner should do the trick.
As far as pre-coats, and "how to apply", you need to follow the directions on the particular sealer you're using. They all have their own specifications.
Many sealers can be painted over, check the specs for your sealer.
Certain local codes do not allow renters to preform any work on their units. Roofing work is dangerous so be careful.