You branch off from the copper tubing with a 1/4" compression tee. Cut out a small section of tubing for which the tee replaces. You must use a tubing cutter to do this, any other method will cause the tube to become oval.
Install the short piece removed on the side outlet of the tee. Attach a 1/4" compression x 1/2" pipe thread adapter to the short section. If you can find a tee with a pipe thread side outlet (preferred), skip the previous step.
Connect a 1/2" pipe thread to hose adapter. When buying parts, ensure the male and female parts mate correctly. If you can't find the proper mates, get a short nipple or coupler to change gender. Use several layers of teflon tape on male pipe threads, wrapped in the direction that causes it to get more snug when the pipe is screwed in.
Attach hose and controller. After all this, there probably isn't much pressure left, meaning you could probably transition from hose to 1/4" drip fittings for the run from controller to plants, keeping the installation less obtrusive. If you use pressure adaptive drip fittings, you can better regulate the flow to each plant, otherwise the first plant will get the most water, the last hardly any.
Be careful, though unlikely in this case, as high pressure can cause drip fittings to blow apart. You also can't use most pressure reducers, as they can spill water as they function. You'll probably have to go from hose to 1/2" drip main to 1/4" drip distrubution. The 1/2 to 1/4 punched connection can leak slightly, so it should be done over the first plant.
It appears as though the portion that pulls out has sheared off from the inside. If you inherited this piece, I'm assuming you don't want to put much in it.
Clean it VERY well with some alcohol or similar (not acetone) and a brush. I'd try some J.B. Plastic Weld, let it setup and cure overnight and give it a shot. You've got a 50/50 chance it will either fail incredibly or someone will inherit it from you.
I've never had much luck with repairing things like this, but the J.B. Plastic Weld (and similar "plastic weld" products has fixed a veritable stable of Fisher Price toys, Big Wheels and similar.
Good luck!
Best Answer
Yes you are supposed to cut this at the point which gives you the correct diameter.
Collecting dust from tools requires large amounts of airflow (cfm) and static pressures can be very low and still effective. In your case, you will have high pressure but low airflow due to that restriction.
Also helps to ensure there are minimum bends and turns in your hose and keep the hose as short as possible.