Step by step (if I can remember them) -
You want to setup your Caseta Pro (and it MUST be a PRO) hub with a static IP. The integration program in Hubitat will want that IP address and it will save you heartache if it doesn't change. Your Hubitat IP should also be static.
In your Lutron Caseta App, you want to enable Telnet Support (gear icon, then Advanced). When you do you should see that IP you assigned static (reserved) as well as your gateway (router), subnet and DNS entries (all should be picked up from your router or DHCP source).
On the Hubitat, you will go into apps and click to Add a Built-In app (upper right corner of the apps page) and select the Lutron Integrator.
This is probably a good time to get an integration report off the Lutron Caseta system. That's also under advanced options. You can view it on your phone or what I do is save it to Google drive so I can save it on my PC . . . whatever works for you.
Back on Hubitat, click to launch the Lutron Integrator and you will get a set of buttons - click to create a new Caseta Integration. You will need to assign a name and also enter the IP address of your Caseta Pro Hub that you found in the advanced section on the Lutron Caseta app (mentioned above).
At this point you can add devices. I do it manually because I don't necessarily add all my Lutron devices into Hubitat. You should be able to find your Pico in the integration report.
There are two ways to enter them - individually (sort of menu driven) and bulk (a list that you type in). I have always used the bulk method and just add my new ones on to the end of the list.
Assuming you use the bulk method, you will enter a pico as p or q (depending on whether you want to be able to use button hold as an option), then the device number taken from your integration report, and then the name of the device.
When you have finished entering the device (or a batch of devices), click Done.
In the Device listing on Hubitat, you should now see a Lutron Telnet device, which is the communications from the Caseta Pro hub to/from the Hubitat Hub and you should also see any of the Lutron devices (Picos, dimmers, switches, shades, etc.) you added through the Lutron Integrator immediately above.
Advanced Topic - the Lutron Caseta has the ability to group Lutron devices together and you can activate them using a single virtual Lutron device. You will see a large number of "Buttons" at the top of the integration report - that's what those are. To use those, you will also want to add (as a Lutron Device when you are adding them to the Hubitat's Lutron Integration) your Caseta Pro Hub as a Device - I believe it will always be Device 1 - and it is added as a Lutron Keypad device. You don't need to worry about this right now - it can be added later.
If you see your Lutron Devices on the Hubitat Device list, you can now include them in some automation rules. Start with something simple to see if they work. If not working, check the logs.