This diagram uses the Common (COM) and Normally Closed (NC) tabs on the limit switches.
When a limit switch is not pressed, it is in the green position -- connection between COM and NC.
When a limit switch is pressed, it is in the red position -- no connection between COM and NC.
It also uses a Double Pole Double Throw (DPDT) switch.
The dashed line between the poles (blue) indicates that they are linked mechanically, but not electrically -- both will be in the middle (shown below), both will be up, or both will be down.
A black dot indicates that wires are connected and no black dot indicates that the wires are not connected.
If the DPDT switch is placed in the "Up" position, current flows from your power supply "-" (electrons have a negative charge so current flows from - to +), in through the "-" tab of the DPDT switch and out the "Up -" tab, through the actuator, through the upper limit switch (green position), in through the "Up+" tab of the DPDT and out the "+" tab, and back to the power supply.
The actuator will go up until it presses the upper limit switch (red position) which breaks the connection and stops current from flowing through the limit switch.
With no current flow, the actuator stops.
Changing the DPDT switch to the down position allows current to flow throught "Down-", the actuator, the lower limit switch (green position) and "Down+" until the lower limit switch is pressed (red position) and the actuator stops.
If neither limit switch is pressed, the actuator can go up or down, depending on the switch position.
This diagram will work with any of these three styles of switches:
1. DPDT 2-position On-On
2. DPDT 3-position On-Off-On
3. DPDT 3-position (Momentary On)-Off-(Momentary On) -- sometimes abbreviated as "(On)-Off-(On)".
The downside to the first two options is if one of the limit switches isn't working or adjusted properly, the motor can reach the end of its range of motion and still have power applied -- eventually burning up the motor or damaging the mechanism.
With option 3, power is only applied for as long as you press the switch which provides a secondary level of protection in addition to the limit switches.
The DPDT switch tabs and attached wires will probably be physically arranged like this.
When in doubt, use your ohmmeter to verify which tabs are/are not connected when the switch is in each position.