I have just replaced an inner tube on the front tire, and discovered it had a presta valve. My old floor pump is fitted for a Schrader valve. I learned I could buy an adapter, however, I decided to buy a new floor pump with a dual nozzle. I opened up the valve on the presta valve by screwing open the tiny nut. I also used the small screw ring to lock down the valve on the rim. I pushed on the side of the nozzle for the presta valve and locked it on with the lever. As I pumped air was escaping out of the other nozzle for a Schrader valve. I took it off and tried again pushing the nozzle down as far as it would go – about 1.5 cm, locked it down, and again found air escaping through the other nozzle. Thinking the lever must be in the up position to push it down, I tried again. This time the nozzle would not push down very far, and air was escaping through the other nozzle. I'm sure I have the correct nozzle on the presta valve (It is a smaller opening). I'm not sure what to do next, and I would welcome any insight. Thank you.
This really depends on the specific model and design of your dual head (i.e. two valve holes, one for presta and one for schrader).
I've seen at least three variations of dual pump head mechanisms:
The locking lever controls which valve is active by the direction it's turned to.
When you insert the presta or schrader valve in the right hole, the valve body itself hits a small lever on the side that closes or opens the appropriate pump head valve. Sometimes this is actuated by the closing of the locking lever.
Inserting the head of the tire valve trips a lever deep inside at the bottom of the valve hole.
Some valves in dual head designs react to pressure, i.e. when plugging one of the valves into a tire with air the pressure closes the other valve. When filling empty tires and the air keeps coming out from the wrong valve, pressing the outer tube against the inner tube valve while simultaneously pumping air creates pressure that opens the correct pump head valve.
So for troubleshooting, I'd first see if your lever can flip the other way. Then, I'd ensure the tire valve is fully seated (pushed in all the way and maybe give it a wriggle as you push it in). Then I'd try putting the other type of valve (presta or schrader) in to see if the switching mechanism can't reset. Finally, I'd gently prove with the blunt end of a disposable chopsticks inside the sides and end of the valve body to see if you can't locate and unstick the switching mechanism.
This all assumes you can't find the manual which would tell you specifically what to do. I find the cheaper dual head designs to be failure prone, I prefer pumps with single "universal" heads such as this Lezyne.
p.s. I'm noting that the black cheapo dual-pump head whose image above I shamelessly stole off e-bay only goes for 1-3 eurodollars, shipped from China. You could just get another one at that price. I'd personally recommend: 1) continuing to use the one you have using a schrader-presta adapter; 2) get a dedicated single-head; or, 3) get a well-machined universal head.
I had been upset with this same style pump for months till I read this. I couldn't get my Presta side to work/inflate air into the tire, only air would come out the Schrader side. Yes, RoboKaren's answer was correct with mine in that when using the Presta valve, it has to be inserted a certain distance into the pump head for it to actuate the valve inside it to switch which direction the air travels on the dual Schrader/Presta nozzle fill head. My Bell pump seems to always stay on the Schrader unless you press it far enough on the Presta stem which moves the valve to allow air not to flow out the Presta side. When head is removed from filling the Presta side, it automatically springs back into position for filling the Schrader side.