You can put together a decent kit for about $60 - $80... a Mighty Vac (or similar) and a blood pressure type bulb are all you need to test both pressure and vacuum.. Seals tend to show problems under vacuum; pressure is great for finding the location leaks (bubbles out).
If you want to be "economical", a cheap autoparts store combination pressure/vac gauge, a hardware store check valve, bicycle pump for pressure, and then the same pump with the internal seal reversed for vacuum will suffice..
Exact test details can be found in any Stihl service manual, but the basic principle is to seal up the engine and then pressure and vac test it. One way is to slip a piece of rubber between the muffler and cylinder, and either a test flange or another piece of rubber behind the carb. Plug into the impulse hose (one of many ways, and saw dependent) and pressurize the engine to about 8-10psi. It should not leak. If it does, spray with soapy water and look for bubbles, or dump the entire saw in a 5 gallon bucket of water. If that all passes, then do the same for vac at -0.4->0.6 bar, and rotate the crank back and forth. It should hold a vacuum, and if it doesn't, it's almost aways seals. Drop some light oil in the seals and it will either get sucked in, or "cure" the problem. If you suspect a seal but it's holding vac, then just prod it a little and see it it lets go. Stihl allows some leakage (time and pressure based), but I like to see a perfect seal.
Testing a saw like this eliminates (or shows), bad boots, impulse hoses, gaskets, seals etc etc... and can save a bunch of experimentation.