Create a plan for all of the boxes you want to connect with conduit. Measure the distance between the boxes and any bends that might be necessary. If there are a number of bends or the bends are tighter than 90 degrees, you should opt for flexible conduit. Otherwise you can use rigid conduit with bend attachments.
Switch off the power at the circuit box. You should never work on live electrical wiring.
Disconnect wires to the circuit box.
Knock out the hole in the junction box to make way for the conduit. Metal junction boxes have pre-scored sections that can be punched out to allow conduit to pass through. If you're using plastic junction boxes you may need to drill the hole. Make the hole large enough for the conduit you purchased. Repeat for all the other junction boxes.
Measure the distance from one box connector to the next and cut the conduit to that length, adding enough to the length for the conduit to slip inside the junction box connectors.
Slip the connectors on the end of the conduit and test fit it in the space between the boxes.
Remove the connectors and file the ends of the conduit so they are smooth.
Insert the connector into the first box and then the conduit into the connector.
Secure the connectors and conduit in place. If using metal conduit, tighten the set screw. For plastic, cement them together following the instructions on the PVC cement.
Mark the spot on the wall where the other junction box's opening is. Remove the junction box mounting screws.
Swing the conduit into place so that it lines up with the mark on the wall. Attach the conduit connector to the end of the conduit and to the loose junction box.
Remount the junction box. Add conduit straps to support the conduit on the wall. One strap for every five feet of rigid conduit is sufficient.
Feed the wiring through the conduit from one box to the next. Repeat as necessary to connect all your junction boxes with conduit.