This all looks wrong to begin with, as in one switch just turns on/off power to the other switch. Do they actually operate different fixtures?

Going to start with the usual disclaimer that if you're asking these fundamental wiring questions, you should call an electrician.

But, if you want to learn and are willing to take the risk, you should start off with buying a digital multi-meter, so you can check which specific wires are "hot". What you're likely dealing with in this box is a single "hot" wire (black) that is bringing power into the switch on the right. From there, you have a black "switched hot" going to a light from your switch on the right. You also have a jumper making a daisy-chained connection to the switch on the left (which is how it gets power). Then from that switch, you have another "switched" hot that goes out to a light. Based on that simple wiring, I'd wager you do not have a remote 3-way switch tied to either of these.

As for your new dimmer, if you look in your instruction manual, a standard single-pole dimmer connection has you connect incoming "hot" to the black wire, the dimmed output to your light is the red wire, the green goes to ground, and the red striped wire is capped. Because both dimmers have black leads, you could tie them together and connect to the incoming hot, if the leads reach.

If you don't have much experience with wiring, I'd again advise a professional, but there are many YouTube videos on how to properly use wire-nuts or lever nuts to make these multi-wire connections. Your scenario here is very basic lighting connections. Make sure to turn off the breaker before touching anything in the junction box. If you need to check which wires are live with the multi-meter, turn off power, disconnect the wire nuts as needed and make sure there is no chance for a short, turn on power, check with meter, turn off power again.

Hey, thanks for the reply. I have a meter. I've wired some things before, but I always had the hot, ground, and neutral. It threw me off that none of the white or ground wires were connected to the switches. So, I tied the incoming black wire to the black on the dimmer switch, the ground to the other grounds, the solid red to the jumper going to the second switch, and capped off the red striped wire.

Yes, one is for track lighting in the living room and the second switch is for the main kitchen light. It threw me off with all the white wires tied together and all the ground wires tied together, but none of them connected to the switches.

Sounds like you wired it backwards. If you're leaving the switch on the right, you want the jumper to connect to the black on the dimmer (left). The red wire from the dimmer should connect to the black romex wire going out of the box (on the left). That black wire goes to your light. Before you actually make that connection, I'd suggest fully disconnecting the switch on the left, capping the jumper, turn power back on, and check the black romex wire on the left with your meter to make sure it is NOT hot. If that wire is dead, with the breaker turned on, then it is most likely the hot wire to your fixture and is the "switched" hot wire.

Also, what "threw you off" is normal for generic light switches. Lights need a complete circuit to turn on. You use a basic light switch to turn on/off just the black hot wire, which breaks the complete circuit to the light. There is no need to also break the white wire, so that's why they're all connected, just passing the neutrals through the j-box out to the lights. The switches should have been grounded for safety, but doesn't affect the operation of them.

I did as you said and you were correct. I connected the black dimmer switch wire to the black Romex wire going to the light. I connected the solid red to the black jumper going to the switch on the right. Thank you so much for the help.