I recommend you do this project in an area without a lot of wind, but with good ventilation like a garage.
Sand
The first thing you'll need to do is to sand the pine wood round to get a smooth base. I would recommend using the 120 grit for rougher areas (the edges of the table), then go over it with the 220 grit paper. For the top of the table, I used the 220 as it is a lot smoother. Remove excess dust with a tac cloth.
Prime & FILL
Spray a thin layer of primer in long strokes with the grain of the wood. Let dry for an hour, then sand with 220 or 120 grit sand paper. Remove excess dust with tac cloth, then repeat steps until you feel like you have a smooth finish. I primed and sanded my table 3 times, but it just depends on your individual results. After the first coat of primer, you will notice that the imperfections will start to show, like scratches, dings, and cracks. If they are not that bad, the primer will fill them in, but if they are deep, you will need to fill them in with wood putty or filler. If you do use wood putty or filler, all you would do is apply it according to the package directions, let it dry, sand smooth, wipe with tac cloth, then add another layer of primer and continue with the process that I've mentioned beforehand.
Paint
The key to getting a smooth finish is to have a smooth base to work with, so I can't stress enough about the importance of sanding as well as removing all dust particles and impurities before you paint. Once you have that covered, you are ready to roll - literally! Working with oil-based paint is a little tricky, but the key to applying it is to not apply it too thick because it will take longer to dry and it will run - oh it will RUN - and you don't want to be like me, stuck sanding it all down again. I learned the hard way.
To apply, use long strokes along the grain of the wood and try not to go over the same spot you painted too many times or it will drag. Since oil-based paint takes longer to dry, it will smooth out, so don't worry too much about getting it completely perfect. I recommend applying paint to the top of the table first, then to the sides of the table (remember, thin coats). Allow your paint to dry completely; dry time will vary by climate. This can take anywhere from 24-72 hrs to weeks, so patience is a virtue here.
Before you apply your second coat, look for any areas where dust or particles may have entered and sand those areas down with 220 grit sand paper. Completely wipe your table down with a tac cloth to make sure you have a clean surface. To apply the second coat, apply as you did the first. Two coats should be all that you need, but it really depends on your preference. I had to do 3 coats, but that's because I messed up and had to sand down the drips from the second coat I did.
Allow your table to dry for several weeks because the fumes will be strong for a while. Oil-based paint also takes a while to cure, but you can still use it. In the meantime, just be careful not to bang it or it will dent. Once it is fully dry, the finish will cure and harden.
Legs
For the legs, I do recommend installing them to your table before you apply the polycrylic gloss. To do this, you will need to first measure your table's circumference with string, which will roughly be 75", then cut the string into thirds (25" each). Using the string that you just cut, lay it out along the circumference of the table. At each end, this is where you will mark your spots for where your legs will be installed. Mark your spots at a 4" depth from the edge of the table. Now you can place your top plates on and get to drilling. Make sure that your top plates are angled outward first. It's a simple step that can be overlooked. Mark all four holes on each top plate as a guide, then drill in place. Once that's all done, you can now screw on your legs.
Now it's time to paint your legs with the polycrylic gloss. I didn't sand mine, but I do recommend you do so to get a smoother finish before you paint. Mine turned out just fine, so it's up to you. Since the polycrylic base is water-based, the wood grain will raise a bit, which you'll either want to sand smooth or you can leave be (which I did). I just used one coat to maintain that natural finish. Let the legs dry for an hour and they're good to go!