There is a chart for a lot of reel makers that lists what type of reel you have and how much backing you should put on. I've seen some as few as 50 yards and some as much as 250 yards. I have one of those charts somewhere...which means I forgot exactly where it is right now, but I can find it given enough time.

If you want, drop me a note and I'll try and dig it up.

This is what I found while searching on the web:
INSTALLING FLY LINE ON A REEL
Install the backing first.
Most fly fishers fill the spool of the reel with as much backing as possible to allow them to retrieve faster and to reduce line memory. Thereby the line is less likely to tangle.
Read the reel capacity chart to determine the amount of backing needed for the reel.
Find and loosen the end of the backing. Remove a few feet of line from the spool. Run the tag end through the front of the reel, around the spool, and out again. Tie a simple overhand slipknot in the tag end, then a single overhand knot, tighten and trim it. This tag end will be tied to the reel with an arbor knot.
The backing should be installed by pulling it off a revolving spool. If the spool is laid flat on the ground and the backing coiled off (as when filling an open-faced spinning reel), it will twist and become tangled.
Place a bunt pencil through the center of the spool of backing, so that the spool will rotate around the pencil
Place pencil between your knees. With the end of the backing tied to the reel, reel the backing onto the reel from the backing spool preferably through your fingers to apply tension while loading the line and to load the backing evenly onto the reel. Stop when enough backing is on the reel.

Spooling fly line
Open the coil pack holding the fly line by twisting and carefully remove the fly line from the coil pack. Remove twist-ties from the line and replace it on coil pack. DO NOT place the line on the floor, because it will cause the line to twist or become entangled. Put the coil pack back together, leaving approximately a foot of line outside the coil pack. Tie the tagged end of the fly line to the backing using an Albright knot.
Insert a blunt pencil through the hole in the center of the coil pack, so that the pack will freely rotate around the pencil.
Place pencil between your knees and spool line slowly onto your reel. Guide line trough your fingers to apply tension and to load the line evenly onto the reel. The fly line should be fully loaded except 4 or 5 feet.
Attach the butt (thick end) of your leader to the end of your fly line using a nail knot.