Find your current location on the map. Find your diversion on the map. Pinch both locations between thumb and index finger so a crease forms between those points. Run your fingers along the crease so it becomes sharper.
See if there's any airspace that you don't want to be in in the way. If so pick a waypoint that keeps you clear, make creases as required.
If there are line features that run in more or less the proper direction, find these line features and fly along them. Even if it makes the flight five minutes longer.
Look at the known wind. If wind from the left, steer left 5 degrees. If wind from the right, steer right 5 degrees. One thumb lenght, from the tip of your nail to the first knuckle, is 10 miles/five minutes. Add 5% if there's a headwind component, subtract 5% if there's a tailwind. Give ETA to instructor/examiner.
Look for waypoints along the way, increase or decrease your drift compensation as required. At each recognizable waypoint, measure the ETA again, give updates to instructor/examiner as required.
It may sound incredibly crude but it's good enough for PPL style flying.
Bonus points for informing ATC (actually a requirement if you're on a flight plan) and getting some sort of assistance, whether that's "flight following" or "basic service" or whatever. Frequency of your destination is on the map, so pre-select this in the COM box early, then locate the approach plates for your diversion and start planning the approach.
More bonus points for using radio nav. If the destination has an NDB or VOR it's virtually impossible (but not 100% impossible) to miss it. If it's got a DME (or TACAN) you'll know your groundspeed and ETE very accurately. GPS, as mentioned, is even easier. In addition to mrmums method, you can also go to the "nearest" page and select the destination from there.
I once witnessed a student do a practice diversion while I was observing from the back. It took him five minutes with the E6B, a ruler, a protractor and everything to plot his diversion. By which time the aircraft nearly entered a spiral dive twice, was of course 10 miles from the initial diversion point with the student hopelessly lost, and during which time zero lookout was kept. Boy, was I glad there was an instructor in the RHS who could fly the airplane in the meantime. The diversion calculation was eventually spot-on but we could've been killed a few times over in the meantime.