Wiring a Junction Box: 1 source in, 2 sources out
Yes, you would tie the hots together, the neutrals together, and the grounds together. Below is an image of the inside of the box for reference.



And here is a wiring diagram as requested. The main line from your breaker comes in at the top of the diagram and enters the box. It is then tied off and sent to the left to your always hot load or other switch and also to the right towards the existing switch and load. (Black is hot, gray is neutral, orange blobs are wire nuts, and grounds are not shown for simplicity)



I've also included a more clear cut version of the diagram so that you can see the flow of power.