Most of this type of lamp originally had a 3 way switch that cycles through lighting one, then 2 and finally 3 and then off for the candle arms. The switches are still available but are confusing to wire. If your light has original wiring, you can use it as a model for the new wiring.
Otherwise, just get a simple on/off switch, (not 3 way). Connect one of the wires from each of the 3 candles to each other. Then connect the remaining 3 wires together from each of the candles together. Now connect one of the lamp base wires that plugs into the wall to one of the sets of wires that go to the 3 candles. Now connect one of the wires from the switch to the other set of wires that go to the candles. Connect the other wire from the switch to one of the wires that comes from the lamp base and plugs into the wall. This will make it so all the candles turn on and off together.
Attach a short length of double stranded wire to the mogul base and then attach each of these wires to the 2 wires that go to the lamp base and plugs into the wall.
I have successfully replaced mogul based lamps with standard lights. You will need 2 things. The turn key that turns the center light on and off will need to be longer. I found a 1/2 inch extension will work. You can get one from this site and screw it onto the existing plastic turn key.
www.antiquelampsupply.com/product/2286_brass-key-extensions
The other thing you will need is a new all-thread that will screw into the base of a standard light socket (widely available in different lengths). The all-thread that screws into the mogul base will be larger than what will fit into a standard light socket. The old all-thread from the mogul base probably screws into the part of the lamp at the center of the candles that hides the connections for the wiring. Instead of using the old all-thread, just insert the new all-thread through the opening where the old all-thread was located and attach it to the other side of the lamp part with a nut. The new all-thread will pass through the opening without any interference. You will probably need some washers (probably one or 2) to be able to adjust the height of the turn key for the light switch to the correct height so it is aligned with the hole in the lamp part.
Otherwise, just get a simple on/off switch, (not 3 way). Connect one of the wires from each of the 3 candles to each other. Then connect the remaining 3 wires together from each of the candles together. Now connect one of the lamp base wires that plugs into the wall to one of the sets of wires that go to the 3 candles. Now connect one of the wires from the switch to the other set of wires that go to the candles. Connect the other wire from the switch to one of the wires that comes from the lamp base and plugs into the wall. This will make it so all the candles turn on and off together.
Attach a short length of double stranded wire to the mogul base and then attach each of these wires to the 2 wires that go to the lamp base and plugs into the wall.
I have successfully replaced mogul based lamps with standard lights. You will need 2 things. The turn key that turns the center light on and off will need to be longer. I found a 1/2 inch extension will work. You can get one from this site and screw it onto the existing plastic turn key.
www.antiquelampsupply.com/product/2286_brass-key-extensions
The other thing you will need is a new all-thread that will screw into the base of a standard light socket (widely available in different lengths). The all-thread that screws into the mogul base will be larger than what will fit into a standard light socket. The old all-thread from the mogul base probably screws into the part of the lamp at the center of the candles that hides the connections for the wiring. Instead of using the old all-thread, just insert the new all-thread through the opening where the old all-thread was located and attach it to the other side of the lamp part with a nut. The new all-thread will pass through the opening without any interference. You will probably need some washers (probably one or 2) to be able to adjust the height of the turn key for the light switch to the correct height so it is aligned with the hole in the lamp part.
