Broken chain pull switch had 2 wires. New one has 3 need to know what to wire to please.

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Typically AC wire protocol designated black = line voltage (means \'death\') and white is neutral (cold).

The blue one will be a switched line to the motor and a meter capable of checking continuity should allow you to determine the proper wiring.

I can offer resources:

1) Test switch that was removed, and test for hot connection to narrow down options.

What speed was fan stuck in when switch was removed? Let's say medium speed.
Which connection at fan is hot? Use voltage tester to find hot connection at fan, and match that up with wire-color on switch that was removed.
One and only one wire on 3-speed fan switch connects to hot. And the hot wire is the only wire that connects to each other wire as switch cycles through pull-chain sequence. All pull chain switches follow same sequence: off, low, medium, high.
Let's say old switch was stuck in medium, and you know which color wire connects to hot.
Test switch with continuity tester to see which wire(s) have continuity with hot wire: some switches, it will be 2 wires, and other switches it will be 1 wire. Match where wire(s) were connected, and map that to tests on new switch.

2) Open following link for illustrations and some other links.
http://waterheatertimer.org/How-to-wire-Cooper-277-pilot-light-switch.html#3-speed

Old switch and new switch have to be compared using multi-meter or continuity tester.
Each 3-speed switch has identical pull-chain sequence: off-high-medium-low.
Each 3-speed switch has only one wire that connects to Hot wire.
But the other three wires can vary.
For example connect power to switch Hot wire. Let's say switch is in off position. Pull chain once for high speed and power might flow to just one wire, or it might flow to two wires, depending on the switch.
Pull chain again for medium speed, and power might flow to just one wire, or it might flow to two different wires.
Pull chain again for low speed, and power usually flows to just one wire.

Easiest place to start is to find which wire is Hot.
Only one wire connects to Hot power.
That same wire on the new 3-speed switch will connect to all other wires. When testing, only one wire connects to all other wires.
Once hot wire is determined.
Then test which sequence of wires receives power each time chain is pulled.
Repeat same test on old switch.
Note how old switch was connected. And then map the change-over to new switch.

Open following link for resources:
http://waterheatertimer.org/How-to-wire-Cooper-277-pilot-light-switch.html#3-speed

You have 2 questions:
1) Pull-chain Switch question:
You need a fan switch with 4 wires.
http://www.homedepot.com/webapp/wcs/stores/servlet/ProductDisplay?storeId=10051&productId=202191016&langId=-1&catalogId=10053&PID=500871&cm_mmc=CJ-_-500871-_-10368321&cpncode=00-29062147-2&AID=10368321&cj=true&srccode=cii_9324560&locStoreNum=577
Your pull-chain switch has one wire that connects to Hot from wall switch. And then one wire for each of the 3 speeds.
Best way to start is to test the old switch with continuity tester.

Compare results with following image of 3-wire switch for general reference:
http://waterheatertimer.org/images/Fan-motor-1-500.jpg

2) Ceiling fan pull chain switch is for the fan only.

It takes 2 testers.
regular tester


Continuity tester has battery and light bulb.

Use regular tester to find Hot wire that feeds old-switch.
Remove old-switch from fan
Strip back wires
Separate wires so they can be tested.
Turn on power.
Test each wire to bare copper wire -or- to green wire -or- to metal part of fan
One of the fan wires will light up tester.
This is the Hot wire.
Mark Hot wire.
Mark which color wire on old-switch went to the hot wire.

Use continuity tester on old-switch.
You know which wire is hot-on-old-switch
Pull chain and test hot-on-old-switch to both of the other wires.
When tester lights up, mark this wire.
Pull chain again and test hot-on-old-switch to both of the other wires.
When tester lights up, mark this wire.
At some point when you pull the chain, the tester will light up both the other wires.
This is the high speed.

Use continuity tester on new-switch.
Repeat the test for old-switch.
Identify which wire will be the Hot wire by process of elimination.
Mark this wire.
Identify high-speed wire.
Pull chain again, and tester lights up on medium speed.
Pull chain again, and tester lights up on low speed
Identify these wires and match pattern to the old-switch

If you need more help, add a comment, and I will answer

I assume the switch operates the lights only. Besides the ground (green or bare) and the neutrals (4 white wires all connected together), the only wires of interest should be 4 wires (black) from the fixture and the 2 wires on your switch. Of the 4 black wires, one of them is the hot wire and the other 3 connect to the three bulbs. Connect the hot wire to either one of your switch leads and connect the other 3 wires to the other switch lead.
If you don't know which of the 4 black wires is hot you can find it by the process of elimination as follows---- connect any three of the black wires together (then supply power), if nothing lights, then the 4th wire is hot. Otherwise 2 bulbs should light. Remove one wire from this trio. If nothing lights, the wire you just removed is the hot wire. Otherwise, one bulb should light and one of these two remaining wires is the hot wire. Take one of those last two wires and connect it to one of the other bulbs. If it lights, then the wire you just moved is hot. Otherwise the one you left behind is hot. I hope this is helpful. Good luck. Be safe! Al K

To replace chain switch with a new one (available at a hardware store), first turn off power to the fan. Unscrew the nut on the bottom of the fan which holds the coverplate in place. Find two wires going to the switch, pull them out of the enclosure, take the wire nuts off. Now you can take the old switch out by unscrewing the locking nuts that hold it in place. Put the new switch in by reversing the instructions for removal.
Good Luck.

playing with power when you do not what is going on = pain or *****
get in an accredited electrician who can do the job in 10 minutes safely

Replacements are available at Home Depot and Lowes. This is a regular 4-wire single-layer switch.

Mark the old wires, so you know which ports they go to in the switch (marked L, 1, 2, and 3) -- then remove the old wires by pressing a paper clip into the hole of each wire while pulling firmly on the wire. Then just push the wires into the new switch, into the marked holes.

I hope this helps! If you have any more questions, please feel free to ask!