To get a close estimate, find out your shaft's "grains per inch" and multiply times arrow length (inches), add weight of nock, insert, vanes and broadhead. Other things such as wrap and lighted nocks can add a little more if you use them. For the most precise measurement, weight everything on a grain scale.
Rough estimate for my setup:
Rear nock & vanes - 40 grains
Broadhead - 125 grains
Aluminum standard insert - 20 grains
Arrow shaft 9 grains per inch @ 29" long - 261 grains
Total - 446 grains
The last few I weighed came in at 442 grains.