I tend to take a very chilled out approach. Generally my clients offer me a drink and we chat for a few minutes, and then, assuming they haven't jumped me already, I suggest that we move somewhere a little more comfortable. Usually they're very happy to oblige, and now that you've initiated the move to the bedroom, I find it tends to move quite smoothly forwards.
This is an approach that works really well for me, too (except it's usually incalls so I offer the drinks). Even though it's mostly symbolic as no one ever gets through a whole cup of tea or glass of wine before things have moved on

I think it's a really nice step to sit down and have a drink with someone. Definitely adds something to the booking, maybe more of a 'date' feel if that's what the client's after, or even a chance to share something a bit boring about yourself so they realise you're a lovely, normal girl and that they don't need to feel shy or awkward. Plus it's just a strong custom in pretty much every single human society since cups were invented, probably, so feels good to start with an interaction you're both familiar with.
Once in the bedroom, I find I have to pay attention to start things off in a natural way - I've gotten so used to having sex with strangers that I forget that for some clients it's actually an unusual occurrence.

But with plenty of careful attention to their spoken and/or behavioural cues, all goes well! And I no longer feel silly when being flirty (not a thing that came naturally to me ever!) since a bit of a giggle can really smooth things out sometimes. I mean, you don't want to put on a whole massive act of pretend flirtation, of course, but just a bit of on-purpose-obvious flirting can be amusing enough to distract one or both of you from any nerves. Plus, I think it's nice to feel like a bit of an entertainer, adds a fun layer to the 'everyday' bits of escorting since you have to tailor the experience to the client to give and get the best result.

Also, as cindy said, give yourself plenty of time to get accustomed to this work as there's no need to pressure yourself to be perfect straight away. At least I hope not cause I'm definitely still waiting for the day I do it all perfectly! Even if I don't say anything stupid or forget to put the kettle on even after they've asked for a cuppa, I will end up falling off the bed trying to get out of my knickers or something. But I've found that sooo much of my confidence has grown over time so I expect more as more time goes on - you can't help but want to improve at what you do, especially when I suspect many other sex workers of being queens of seduction and I secretly panic about the competition!