All you need is an informative tutorial on which tools to use and how to.
Lucky enough,BRIGHT SIDEon YouTube offers this helpful guide.
This is where lint rollers can get really handy.

Image Credit: BRIGHT SIDE via YouTube
Simply roll it over the speakers to remove all the dust and dirt.
This can help clean hard-to-reach areas easier.
Remember to not wet the toothbrush, and gently drybrush in a circular motion instead.

Brushing too hard can only push the dirt deeper.
This method can also clean without damaging a sensitive area as your phone jacks.
Remember to turn your rig off before cleaning.

However, liquid crystal displays need a different cleaning method.
A mixture of distilled water and white vinegar in a 1:1 ratio on a spray bottle can work wonders.
Turn off your rig, spray the solution on a soft cloth and wipe it on your screen.