I just started working as a server, First 2 days have been pretty bad but it’s already gotten immensely better. I totally understand when you say “learned” I don’t really have set phrases yet so I have to think about what I’m saying, it makes it a lot harder. For all of my speaking jobs(I’ve had a lot), my technique is to preoccupy my mind with something else while I speak to people. Here’s how I would approach the situation you mentioned- you notice a group just sat down at a reserved table, first thing is walk over immediately, don’t give yourself time to overthink or anticipate, almost surprise yourself. As you’re walking over, look at the other tables, notice table 40 needs a refill and 45 looks like they’re ready for their bill, your friend might need some help clearing their table. Now that you’re at the table just tell them “hows it going guys, I think that table is reserved, can I seat you somewhere else?”(or whatever you wanna say) Once they say yes, you’ll be looking for a new place to seat them or passing it off to the host, so your mind will be busy doing that and it should be smooth sailing. Another thing I’ve learned in only 2 days, certain formal or pleasant language can be hard for me, but I’ve noticed I can say something slightly less polite if I make up for it with my tone and smile.