Budman72,
I am not knew at this at all, and had the same problem. I grew up on farm tractors that the PTO easily spinned on and making the connection was simple, just turn the shaft by hand (by a few fingers, actually) a little and on it went. And no, we never even thought about shutting the tractor down when performing this maneuver. With my L3010DT, the PTO shaft does not turn, there is some kind of resistance you can feel when the tractor is running. It will turn but only by grabbing firmly with both hands. Not possible when trying to align splines. I think it is the PTO break that stops equipment from freewheeling when you shut the PTO down. With the engine off it turns more freely, but not like the 2 farm tractors of my Dad's, they don't have a break. A smart operator doesn't really need one, they use the engine to slow the equipment down to idle, then shut it off. From an idle everything will stop running in just a few seconds.
On the L3010DT, the PTO is hydraulically engaged, with the lever at the right rear corner behind the 3ph control. What I do is study the splines on both sides of the connection and bump the pto shaft just a touch (easy enough with the control lever, from behind the tractor) until the splines look to be lined up. After one or 2 bumps, I usually have things lined up enough that it goes right on. I would prefer to be able to freely turn the shaft by hand, but this works for me. I exepct it is highly tractor dependent, though.
On my brush hog I can usually turn it a bit by hand to get it to line up, can't be done on my finish mower, to much to turn.
Whatever technique works for you, be careful. If you are not comfortable making the connection with the engine running, don't do it. Personally, I am not phased in the least by making the connection with the tractor running. But that's me, and I am a certified explosive handler at work, so risk is not something I take lightly.
Nick