There are a lot of different methods of doing this, but one commonly used technique is to lead a line aft, outside of the lifelines and shrouds, to the cockpit and to drop the anchor or pickup the mooring from there and then walk the line forward as the boat falls off and goes head to wind.
Last week sort of tried as SD suggests.. however the wind andcurrent were at odds and I made the mistake of trying to pull the boat against the wind from port midship where I was and the current coming full rip of low tide on the bow. the pick up stick fell over the lifeline and that quick I almost broke a wrist or arm when the line wrapped around my hand as the wind gusted and drove my boat to starboard.... thank goodness the lifeline and pick up stick unwrapped and I just came away with mud all over my white shorts! yes, it was mud this time! And.. a pulled out brace on the stanchion. whew.. close call that was!
Is this your boat or some one else's? The reason I ask is that if it's your boat, you should get the feeling for how it handles.
Anyway, on my boat, to pick up the mooring, I head upwind to the mooring. When I'm 10 feet away from the ball I just walk forward and grab the pick up stick. I will carry a boat hook with me, but I don't usually need it. Occasionally something goes wrong and I have walk back to the helm and go around again. If it's real windy the key is to get a mooring pendant (there are two on my mooring) onto a deck cleat real quick. Then you can take your time with everything else.
It's basically the same thing for anchoring / leaving an anchor. To drop the anchor I stop the boat, walk forward, drop the anchor and wait for the wind to blow the boat back until enough scope is out. Then I'll snub the anchor, walk back to the helm and set the anchor.
Retreiving the anchor is easy - I start the engine, uncover the sails, and pull the boat forward until the anchor breaks out, quickly raise and stow it, then go aft and motor away. To be honest I have never had to raise anchor in windy conditions by myself.
If it's not your boat and you don't have a feel for how the boat handles, leading a line aft is probably the best idea.
My boat's a 28 and I do exactly as Barry says. It probably helps that I learned to sail on an engineless boat and spent a lot of time practicing picking up moorings under sail. Even though I don't have to anymore, I routinely get underway from my mooring and pick it up again under sail alone. The only time I turn on the engine is if the wind is so light I might lose steerageway in the crowded mooring field.
Practice, practice, practice and it gets (relatively) easy. Then you get cocky, screw up in an embarrassing way and practice again.
I am not fond of the pick the mooring buoy/stick/pennants up in the cockpit area for the following reason: You can run over your tackle and snag it on the propeller or keel or crash into a boat. I have seen it done. DeniseO30 also shows you that things can go wrong quickly.
Often the mooring buoy and pick up stick with pennants are 5 to 8 feet apart. The mooring buoy doesn't really move a lot, since the heavy chain anchoring it to the bottom/block doesn't move around unless there its load on it, whereas the buoy/pennants float around with the current/wind. So in some instances the buoy can be "far" way from the pennant ends.
Most people will run only one line from the cockpit to the bow, traditionally on the starboard side. But what happens if, to pick-up the buoy on the starboard side, you need to put the bow of your boat between the mooring buoy and pick-up float/stick so as to have the pick-up stick next to the rigged line. By the time the stick is far enough down your boat length, the pennants are now under the boat maybe caught on the keel. If the disappear under the boat AND your prop is still moving, you could snag them or the top chain with the prop.
Okay, your smart though to rig up two lines so now you can approach from the side that won't cross over the pennants if that is an issue. If your boat is long enough, the wind/current is strong, and you're in a tight mooring field, the boat in front of you my too close to allow this maneuver. Because by the time the pick-up buoy is back near the cockpit, your bow may have crashed into the boat in front of you. Remember once you are on your mooring, the weight of your boat will pull the mooring top and bottom chains taunt and your will settle much farther away from your neighbor.
My approach is very much like BarryL's. I motor into the mooring in the same direction as my neighbors are aligned on their moorings. Sometimes this is into the wind, sometimes its a combo wind/current. I eyeball when I am about a 1 to 1.5 boat lengths away and put the motor in neutral. I point the bow directly at my pick-up buoy, not the mooring buoy. I quickly walk forward and ready with a boat hook and my hand. As soon as I can reach the PU buoy, I drag it on board and throw one or both of the pennants on my cleat. If the boat is still moving forward. I quickly go back the cockpit and put the motor in reverse for a second or two to stop the forward progress. If a leave it short and I can't reach the buoy, I head back to the cockpit and go around again.
If I do it right, I don't need the boat hook, but some times the buoy is just out of my reach, and the boat hook allows me to get it. If the PU buoy is more than a foot or two out of my reach, I go back to the helm and go around again.
After 30 or 40 tries, I have a pretty good idea how the boat slows in various/wind current conditions. If there is absolutely no wind, I may put the boat into neutral at 2.5 boat lengths, very wind, 3/4 of a boat length.
I also agree with Barry, but suggest that you get an extra-long boat hook to help you when picking up a mooring. Your boat hook might seem long enough, but when you're standing or kneeling on the bow, it uses up a lot of it's length just reaching down to the water. A long boat hook will reach a little farther, in case you don't get as close to the mooring as you'd like, and might save you having to go around for a second try.
I had the rope caught up in the rudder / skeg gudeon before, while trying to pick up a mooring , from the cockpit. After than, I decided to do like Barry, walk up from calmly, but quickly, once about 15 ft away, with a bit of speed on. Once you get the mooring hooked, it will bring the boat to a stop anyway. If you can't grab it, you can walk back to the cockpit, and as you still have steerage, you can circle around, and try again.
One big recommendation - forget the normal wimpy, plastic marine boathooks. Go get yourself a pike pole / tree trimmer type wooded pole, with an attached metal hook. After breaking one plastic pole, quite easily, I have enjoyed using the more rugged one. I aim the boat in between the mooring ball and end of the floating line, so I have enough slack to bring it aboard, and cleat it quickly, before going by it. Don't worry about feeding it through the chock / cleat properly. Just do a couple of figure 8s on the cleat, wait till the boat stops, then pull some slack, and do it properly.