Now we bust out the fretboard oil!
This is a very easy and cheap thing you can do every time or every other time you restring your guitar. There is no reason you need to pay someone to do this for you.
For this I'll use my lemon oil and rag. Apply the lemon oil to all the frets and remove all the dirt with the rag. Make sure to really get in there and remove all of the oil.
Any oil left behind will collect more dirt and dust right away.