There are hundreds of ways to do all these things.
The best advice is to keep it simple stupid (KISS). That's the best mnemonic.
I find that using FS 2004 or similar is perfect and bash the procedures out over and over, even if they're not the ones you're going to do, you'll still learn alot.
As for DME arcs, I've seen people use so many different techniques, but I keep it simple. If your goal is to fly say a 10d arc, once you've got a rough idea of your starting heading, simply turn by 10 degrees everytime the DME ticks up by 0.1d. If it keeps increasing, turn 20 degrees next time, and if it decreases too much, only turn 5 degrees next time. It works a treat and compensates for wind. I've used this technique in C152's and Medium Jets and it is the best technique in my opinion because it is so simple.
Just a little tip with the holding procedure, if you run out of time to calculate your 3 times drift for your outbound, simply work out your gate and when you get to it, fly up it, compensates for you. Again, keeps it simple. If you know which way the wind is from, simply throw some heading correction in and you can still fly up the gate, show's you've thought about it.
As for entry to a hold, that's just practice at working it out. Personally with practice, I've become quite good at visualising off the approach plates (if the hold is published).
A lovely mnemonic I use as I enter a hold is TTTTT or 5T's:
Time (start your stop clock)
Turn (turn for your entry)
Throttle (set pwr setting for speed to fly hold)
Tune (set up any nav aids needed and not already set up)
Talk ("Aircraft 123 entering hold")
Hope this helps