For the diversion, here's a couple of points:
You should have a few minutes to plan it, so don't be tempted to turn onto some random heading off the cuff; plan a point you will divert from (ideally an easily identifiable spot a little bit up track from where you are now). That will give you some time to work out a decent heading and ETI for a starter.
If an immediate divert is required, pick what you think is a good heading, turn onto it and note the time and the heading on the map. Then when the confusion dies down a bit, you will be able to plot where you started the diversion leg from on your previous track, if you haven't had time to before turning.
Always consider FUEL and airspace, as well as the terrain you've chosen to divert over (obviously a vital issue for IFR because of revised LSALTS, but also for VFR if you start heading over tiger country without thinking about it first).
Get a lot of practice at estimating tracks off the map by eye, and check yourself with the protractor. Also get used to drawing the new track in whilst flying, one-armed paper hanging, but you should be able to get a decent straight line on the map without too much trouble. You can then measure off the track and distance. Some people I know fold their maps on the line from divert point to destination and run a pencil along the fold, that draws a straight line for you.
A rough checklist could be something like this:
1. Where to divert from.
2. Where to divert to.
3. New track, heading and distance.
4. Estimated time interval for the new leg, and select an appropriate altitude for the new track.
5. Have you got enough fuel? If not, better come up with an alternative plan (go somewhere else, find nearest suitable...)
6. Figure out your radio call to ATC or flightwatch if required, or other means of having SAR coverage. Make the call.
7. At the divert point or time, turn onto new heading.
8. FCLEAR check.
9. Plan for a pinpoint or two on the new leg, and familiarise yourself with the features you should see along track and at subsequent turn points.
10. Navigate normally, just like on your planned legs.
11. When you have a spare minute, check your work.
12. Expect the (unexpected) engine failure!