If I have it right the, one near the center is the end of the second wheel pivot. This wheel is usually at the center of the movement so I am guessing you have a center seconds watch. . The one further off center is the arbor for center shaft for the mainspring. In winding, it is turned to wind the spring from its center.
The winding wheels are under the dial as is the click. If there is release, it is a lever under the bezel. If not, you will have to remove the dial.
The dial is probably held by screws from the outside edge of the movement locking dial feet in place. If so you will have to remove the case screws. These are the two spanning the movement and dial edge. With these out, you can lift the movement from the case from the dial side. This will give you access to the dial screws.
Some dials are secured by a friction around the rim and can be removed by prying them up. The movement can stay in the case for this.
Do not try to pry it off unless you know what to look for and how to do this. If the dial is held by feet secured by screws, prying will break the dial. It happens a too often.
Once you have the dial off it is easy to find the release click. Many Englishes watch wind with a bevel gear at the end of the winding shaft. You will see this if you remove the movement from its case. This arrangement makes it tricky to control the let down of the spring. If you have the movement out , return it to its case to engage the winding crown.
Then, hold the crown as you release the click, to let the spring down gently.