Pre-fatigue is a workout technique which means to use a isolation movement immediately before a compound movement. The idea is to further hit the desired muscle group at a greater intensity. For this routine the isolation exercise will be lateral dumbbell raises and the compound move will be dumbbell shoulder presses.
Start by doing a set of lateral dumbbell raises with a weight that will allow you to complete a tough 10-12 reps. The weight should be heavy enough so that your last rep is all you could finish before needing help. Once you finish immediately reduce the weight by about 30 % and do a set to failure for as many reps as you can. Again reduce the weight by 30 % and do as many reps as you can. Now rest 1-2 minutes before moving on to the compound movement.
For the dumbbell shoulder presses you want to chose a weight you could complete 10-12 reps with. Most likely the weight will be lighter than you would normally use due to the muscular fatigue you will be experiencing. Now just like above take the first set to 10-12 reps, then reduce the weight by 30 % and go to failure, and then reduce by 30 % again and take to failure. I would use this routine every so often and would not work your shoulders a good 2-3 days after this.