Capacitor connections wires pulled of capacitor, need to know which wires got to which terminals

if it is a capacitor ( name will be on the unit) there will be 2 wires
there will be 2 terminals ( or 4 terminals that you can see as connected as sets of 2 terminals ) one wire will go on one terminal (connected or not and the other wire will go on the other terminal ( connected or not
the particular terminal for each wire is not important as long as you do not have both wires on the same terminal if connected
in reality a capacitor is just two plates separated by insulation and wound up tight and put into a case
so one terminal for one plate and the other terminal for the other plate

Not easy to explain. The capacitor is split, it has two values, or like two capacitors connected internally with a center tap between them. Two capacitance values, maybe 5uf and 20uf, the lower value for the fan motor and the higher for the compressor, with terminals C-common, F-fan, M-compressor.
Capacitor terminal C is the center tap and that takes 3 connections, line (power) - fan line common to capacitor, and Compressor line common to capacitor. Notice the fan and compressor have a power line not common to capacitor, just power line.
Capacitor terminal F has one wire connecting to Fan terminal C, fan may have three or four terminal writes, two for power with one power being common to capacitor connection and the other power alone, two power connection wire leads. Fan motor third line is capacitor, connects to the capacitor alone. Four wire configuration fan motor is not likely your needs. Omit or ask again for further explanation.
Compressor is similar to fan, only with a capacitance value higher than for tha fan motor. Two power leads, one straight power, the other power lead connects to the capacitor power. The third compressor lead connects alone to the capacitor.
The with is to draw a diagram and level the colors of each lead and terminal lavels too. The motors nameplate may indicate wire color code, the a-c nameplate wiring diagram may be present in the control wron wiring compartment, the goal is to find clues or to trace each wire and verify what they connect or do, take notes on your drawing.
Basically the motor has three terminals, L1 - L2 - C, or C- S-R (Common, Start,Run)

Your new fan motor should have a diagram with it or at least printed on the side of the motor, that will help a lot from your end. As for me, I don't know what unit you have, so I will try to help you with just the basics.

Your old motor probably had 3 wires. One went to the contactor, that is the "Line Voltage", one went to the Common terminal on the old capacitor (COM), that's the other "Line Voltage" wire, and the last one went to the "FAN" terminal on the old capacitor. The reason the old capacitor looks different is because it works for both the compressor and the fan motor (split capacitor). You still need this hooked up for the compressor to work.

The new fan motor.
These vary in brands and wiring so I can not tell you the colors without knowing exactly which motor you have. On the new motor wiring diagram, you should see the "Line Voltage" as described above that 2 of the wires are ran to each other (just on the diagram, not wired together on the unit). This is your power wire that goes to the contactor on the unit, usually black, and your Common wire that runs to the capacitor. You can still run this wire (COM) to the common terminal on the old capacitor since you still have to use the old capacitor for the compressor and the common terminal should still be jumper-ed from the contactor to the (COM) terminal. Then you will probably have 2 wires for the new capacitor, usually Brown and Brown/White. These wires run to each side of the new capacitor and doesn't matter which terminal. Then you will take a new jumper wire from the (COM) terminal on the old capacitor to the terminal on the new capacitor that has your Brown/White lead. Make sure you secure the capacitors inside the unit so not to touch anything surrounding them. Your new motor might also be a "Reversible" motor that has reversing wires also. Again, your new motor diagram can tell you how to hook these up. You have to have it spinning the right way, most of the time it is CCW (counter-clockwise).

I'm sorry I can't be any clearer on this, but without knowing the brands, models, etc, I'm in the dark. If you need any additional help, I would be glad to help! Good luck and hope you get to cooler days!

All the terminals are connected together so it won't matter which terminal you use, just as long as you have the Herm, Com, and Fan wires correct. Hope this helps!

Did the old fan use 4 wires or 3 wires. If it used 4 then connect the brown and brown/white to the capacitor. Then connect the Black to L1 and Purple to L2. If it used 3 wires then tape up or put a wire nut on the brown/white wire. Connect the brown wire to the Fan terminal if the capacitor has 3 terminals or to either side if it only has 2 terminals. Look at the motor data plate. It should have the wires labeled on it. Purple should be the run wire, connect it to the Comm terminal of the capacitor if it has 3 terminals or the opposite side from brown if it has 2 terminals. Another wire should go from this connection to L1. Then connect the Black wire which is common to L2. I hope this isn't too confusing. Let me know if I need to explain it better. Also if the motor data plate says that Black is run and Purple is common just adapt the instructions above to the wire colors.

Sorry it took a while to get back to you; I had to leave for work. Sounds like you have a capacitor with 3 connections on it. Common, Herm, and Fan. It should be connected as follows. One line from the contactor should connect to the common terminal on the capacitor. From the fan, the brown or start wire should go to the fan terminal and the orange or start wire should go the common terminal on the capacitor. The black or common wire should go to the other leg of the contactor(not the one connected to the capacitor.) For the compressor, the purple or start wire should go to the Herm terminal and the red or run wire should go to common on the capacitor. The black or common wire should go to the same side of the contactor as the black wire from the fan. Let me know if this is too confusing.

You should have:

one wire from the compressor that will hook to "HERM".
one wire from the fan motor that will hook to "FAN"
one wire from the relay ("hot" wire") will hook to "C".

Before attempting any of these recommendations, First disconnect all the power sources and check your wiring diagrams on the motor and condensing unit.
On the old capacitor if you look on the top near each of the three terminals. Are they marked, fan - C - herm? If they are that is a dual capacitor and that needs to stay because that is also your compressor capacitor.
The Red wire from the conductor is Run and it's connected to C on the old capacitor.
Follow the Yellow wire and see if it goes to the S or start terminal on the compressor, if it does then that is the Start wire for your compressor and it connects to herm on the capacitor.
For the fan motor a lot of times the wiring connections are printed on the motor label.
Check the label, Purple should be run and connect to C on the old capacitor.
Black should be Common and it connects to the opposite side of the contactor as the Red wire. If the Red wire connects to T1 then the Black wire connects to T2.
The Brown wire shoud be the start wire on the fan motor and it connects to the Fan terminal on the old capacitor.
Now if you want to use the new fan capacitor. Take the Purple wire from the motor and look for any marks (red paint or a dash) on or beside the terminals on the new capacitor. If there is an identifying mark then connect the Purple wire to that terminal, if no marks you can connect it to either terminal. Then you need a jumper wire from C on the old capacitor to the purple side of the new capacitor. Then take the brown wire and connect it to opposite terminal of the new capacitor.

The wiring on these is pretty straight forward

Basically a contactor, either DPST or DPDT, depending. Input power connects here.

Compressor C terminal connects to one side. R terminal connects to the other. 1 terminal of the run capacitor connects to the terminal with the R terminal of compressor. The other side of run capacitor hooks to S terminal of compressor. One wire of condensor fan hooks with compressor R terminal, the other condensor fan lead hooks with compressor C terminal.

Only things missing from all this is a hard start kit and crankcase heater. Let me know if you want to know how to hook those up.

first take all the relays and capacitor off of compressor , then attach black wire with terminal on "C" terminal post usually top terminal, white wire with terminal goes on "S" terminal post on compressor, red wire with terminal goes on "R" terminal post on compressor. then take the two black wires one connects to white neutral wire and the other connects to the black power wire if tis fridge has a condensor fan then you will also need to connect it two the two black wires also thanks hope this helps