Depending on how big it is you can always send it to Gemini, we have them laser-cut smaller acrylic panels for us all the time. The edges are ready to go then.
If you're going to do it yourself, it's critical the cut edge you start with is as smooth as possible. If you can, have it cut on a router instead of saw cut it. Either way, sand the edges with progressively finer sand paper until they are as smooth as possible. Spend a lot of time here, this is critical. The smoother you sand it, the less you have to flame it, which is good.
When it's sanded, use a tack cloth to remove the dust and then start flaming the edge. A blow torch is perfect. Go quickly and make many many passes, don't try to get it all in one slow pass, you'll bubble or melt the plastic. Eventually the edges will polish out nicely.
What you want to avoid is over-heating the plastic. The hotter it gets, the more likely you'll get tiny bubbles in it or it'll deform. I don't know the chemistry behind this, but if it gets too hot the acrylic can also react to solvent cleaners and craze or crackle on the surface. Don't ask me how, but it's happened to us several times, and our local plastics distributor says over-heating the plastic changes it's molecular structure and causes it.
It's a simple process, just fairly labor intensive. Budget a couple hours labor at least to do a decent sized panel. We just finished a 2'x5' piece yesterday and the polishing took about 2 hours, but we didn't have a ton of sanding to do on the edges because we router-cut the shape.
But seriously, if they're not huge, order from Gemini.
