Let it hit the ground whenever possible. If the natural grass is so deep that the coin will disappear or possibly land on edge (or you'd be tossing into mud), then you have no choice but to catch it. If you must catch it, catch it flat with both hands - do not turn your hands over - and reveal by lifting the top hand off the coin.
One way to avoid having the coin disappear in the grass or having it land on edge is to use a large coin - nothing smaller than a silver dollar. Even better to get a dedicated flipping coin (not currency). They tend to be a bit oversize, are easier to see, and offer a little bit more "ceremony" to the event. And they don't fall into the grass as easily. Your association might consider having a custom coin struck for this purpose. You'll pay a one-time set-up fee, and then have some cost per coin, but it makes for a nice experience for everybody.
To make it even easier, I add a little color to each side of the coin (different color for each side). My coin has a helmet on one side (heads) that I fill in with red, and a snapper - seen from his back side in snapping position (tails) - on the other side that I fill in with blue.
When you let it hit the ground, toss it out in front of you a step or so, and have your umpire pick it up for you while you carry on with the captains choices. Makes it a little more efficient. But, you have to be sure you have a trustworthy U, or you may not get your coin back!
And, by the way, the coin toss is not a time for a lecture on sportsmanship. If you have a field mic, go ahead and flip it on. Just have the captains introduce themselves to each other (handshakes), introduce yourself, and then get right into the toss process. Verify which visiting captain will call the toss, show the coin (both sides) to the captains, get the visiting captain's choice BEFORE tossing the coin, verify that choice with the home captain ("He called heads, correct?"), then pause briefly and toss the coin. Announce the results ("It's heads - you've won the toss.") as you place a hand on the winning captain's shoulder, and get his choice. (Before bringing the captains out, the escorting officials (R & U in Texas, crew of 5) should have asked the calling captain what he plans to do if he wins the toss, if the opponent wins and defers, or if the opponent wins and elects to receive, so there isn't any confusion, and we can help them out if they do get confused.) If the winner defers, step to his open side, place a hand on his shoulder and announce, "North High has won the toss, and defers to the second half." Then turn to the opponent and get his choice, i.e., confirm that he wants to receive. If he says anything other than receive, put on the brakes and make sure he understands what is going on. If he still insists on defending a goal or (heaven forbid, kicking), switch off your mic, and take the time you need to make sure that is what his coach wants (which 99.99999999% of the time will be receive). Then (with mic back on) confirm which end of the field the other team wants to defend, have both sets of captains place their backs to the goals they will defend, step to the pressbox end of the receiving team captain, signal and announce, "South High will receive." Then dismiss them with something like, "Good luck fellas - have a great game." Switch off your mic.
Sorry. I didn't mean to patronize or lecture. I just had some time to kill, and wanted to ramble. I do enjoy this so.
Robert