how do i get artifact points

Read this, and you will know everything. If you come back and ask another question, I will know you didn't read it, and I will not help you again.
Galaxylegion.com/wiki

How much artifact points should I accumulate before collecting?

depends on what your current cap is at, and what artifacts you want a chance of getting...

for a chance at all 60 possible artifacts available from arti points (including the mass storage pods), always pull an arti when your points are at or above 20K
to eliminate mass storage pods from the list, pull artis when your points are between 5K and 19,999 (continuum beacons cost 5K points)
to eliminate mass storage pods and continuum beacons from the list, pull artis when your points are between 4K and 4,999 (rescued prisoners and warp gate chassis cost 4K)

here's a list of artis and points required to get them
http://j.mp/APartis

Ok awesome reply, thanks a lot!