You can buy nanometer tips but they are pricey. Each tip costs about $100 and you must buy a pack of ten. 

I would like to go some other way, much cheaper. (As I don't know if I could make one)

The cheapest way to fabricate AFM-tip is using Tungsten wire and NaOH solution.

I bought 100mg of Sodium hydroxide (NaOH)

100ml of tap water and 8mg of NaOH(two tea spoons), and we have a solution, yeah!

Place it in some unused glass cup, made a anod using copper loop of diameter  about 2cm anod (copper wire  of 1.3mm). 

Attached about inch of Tungsten wire(0.25mm diameter) (cathod) and dipped cathod and anod into the solution.

Connect Tungsten wire to plus and copper loop to minus. (If you see a lot of bubbles and 100mA you probably connected wrong polarity) In my case I see a little bit of bubbles only on copper side. After 30 minutes I got some results. (Clumsy me, I managed to drop it when inserting to a microscope, so the tip looks bend)

Will continue next week to get better results.