Jump into Ultimate Footy, then go to Players > Players Market.
Then there's a little Edit Icon next to the available players, then you Sign and Delist another player (unless you have a free LTI slot, then you can just sign player without delisting)
You can put multiple requests in and they will be processed in order. So if you put a claim in for Hannan and it's successful your RFA order will move to back to 18, then once everyone else has their turn it will see if the player you requested at 2 is still available (I think @redbull needs to fix the RFA order though)
Unfortunately in UF there's no way to re-order your claims, so if you have 4 lined up and you want to re-order, you have to cancel them all and re-order by doing the 4 again.
They will then get processed by the system at 12am ish Friday morning, then the players are Unrestricted where you can just sign them without going through the waiver/order process (and wont affect your RFA order). The players are then locked before bounce.