How do you make two different time signatures next to each other but only one actually comes into effect

It's not clear what that would mean, but anything you can do in this regard is done in time signature properties. Depending on what you actually want this to do and mean, you might also need to add a symbol from the Symbols palette. If you attach your score and describe in more detail what the notation is supposed to mean, we can understand and assist better.

"How do you make two different time signatures next to each other but only one actually comes into effect?"

There are two methods:
A. Change the Appearance of the time signature, using the Properties button in the Inspector.
Advantages: really simple to implement; robust to any layout changes
Disadvantages: does not work with C (common or cut-common time signature); does not allow any separation between time signatures

B. Use a normal time signature for the first time sig, and implement the second time sig. using separate digits from the Master palette's Symbols section (search for time).
Advantages: does work with C (common or cut-common time signature) as the first time signature; does allow extra space between time signatures
Disadvantages: horribly complex to implement; requires first digit symbol to be attached to a pre-placed note (or rest); extremely fragile to any layout changes