Proper break in of a 2-Stroke Engine. This a VERY common question and can be summed up with one sentence: Increased Load over Decreasing Time. What that implies is the engine needs LOAD for proper marrying & seating of components and the load should be increased over a reduced schedule.
How this would normally work:
1 - ALWAYS start with 100% NEW fuel and a PROPERLY LEAK TESTED engine per factory guidelines. Carb(s) / Injectors MUST be clean, filters replaced and hopefully if there was a failure you have isolated and corrected the root cause before simply replacing parts.
2 - Heat cycle #1 - Start the engine and bring it to just UNDER operating temp and then let it cool COMPLETELY (i.e. overnight) Ensure it is oiling! Revving the engine BRIEFLY and not over 1/3 throttle once or twice is fine.
3 - Heat cycle #2 - Check for leaks. Pull spark plugs and verify relatively dry cylinders. Start engine and bring to full operating temp and note cooling system burping and top off as needed. Let engine cool COMPLETELY again.
4 - First ride should be SHORT (15-20 min). This is where you will be putting the first load to the engine by applying short / brief bursts of throttle up to 1/2 throttle and slowly rolling into and off the throttle varying the LOAD. Again let cool completely and check bores/plugs , cooling system, and ensure oiling. After this you may ride as much as you wish but NO LONG WOT for the first tank and varying throttle and loads for the next tank full.
Snowmobile specific info:
1 - With most later Ski Doo Etec's you MUST have the ECU put in break-in mode (anyone with a professional BUDS interface can do this). DO NOT add premix to any Direct Injection (ETEC) engine.
2 - Carbureted engines CAN use premix during break-in however no more than 100-1 and the oil MUST be premix-compatible.
3 - Any cable actuated oil pump (Earlier Cat, Polaris, Skidoo, etc) you may find it beneficial to shorten that cable adjustment to allow more initial oiling just remember that it does NOTHING additional at WOT. On the Polaris 800's this adjustment can be left for the life of the engine as Polaris ran these engine VERY oil-lean.
4 - Its ALWAYS a good idea to measure/monitor and CALCULATE YOUR OIL RATIO being used! Fill both tanks then after usage measure the top off amount of each (gallons to ounces) and calculate. This will give you piece of mind that all components are operating properly