You will definitely not be sitting in a dirty environment when applying your screen protector, however, dust particles are an unavoidable phenomenon. There are 2 clever methods that you can use mitigate dust particles that can easily get trapped under the film once applied:

Boiling Water
Boil enough water to fill up a glass full. Place the glass as close as possible on the table near the application area. The steam will help detract the dust particles from the surface of the screen. A proven practice, but be very cautious you don't burn yourself!

Sticky tape
Expose some sticky tape, roughly 10cm long to the air, and as close as possible to the area of application. This will help in attracting dust particles stick to the surface of the tape.

Don't apply the screen protector on you laps or when sitting on your bed! Use a table/desk while comfortably sitting on a rigid chair. Some devices require extra concentration when aligning the holes and therefore if you are shaky you will not get the desired alignment.

Make sure the lighting is sufficient where you can see all the details of the screen protector film and device sensors. Avoid sunny areas during application as the excessive light can hinder application due to shadowing effects.

Make sure your hands are clean and dry. Oily hands may leave grease and smudges on the screen and the adhesive side of the film thus hindering the adhesion.

If you struggle to position your screen protector for a perfect alignment, use an elastic band round the screen to accurately position the protector in place before sticking the alignment tabs.