IME the bit you need to think about most is what you do when you get to your destination.
Presumably you will have your expenses paid, so you can get a taxi from the airport to your hotel.
Some hotels will arrange transport for you, but you'll have to enquire about that first, and then book it - and make sure you have a contact telephone number for the taxi firm as well.
If they don't offer that service, then get an airport taxi - make sure it's a genuine service - there is usually a taxi queue outside the airport, which will be signposted. Often there's an official there, managing the queue and they will tell the driver your destination.
Make sure that you have your hotel name and address on a piece of paper, so that you can show it to your driver. (And don't make the mistake I did when I went to China of only having it in English, rather than in Mandarin!!!)
Official taxi drivers usually do know where all the bigger/international hotels are, so you should be fine. But sometimes - like China - they don't always.
It also helps if you have printed off a map of where your hotel is, with directions from the airport, just in case. (I've actually needed this, but it makes me feel safer to have that).
And obviously make sure you have enough cash to pay the driver. When you get currency from your employer (or a bureau de change if you have to organise it yourself), make sure you get smaller denomination notes so you won't have to faff about waiting for change. And always, always check the meter on the taxi - that it's been switched on when you start your journey. And get a receipt for the amount you have paid.
Sometimes airports offer a system where they will give you a pre-printed receipt, so you know exactly how much your journey is going to be.
One other thing to try and do, if you can, is a bit of sightseeing in your destination - if it's trips to Europe you probably won't have any or much spare time, but a guide book to the city/place you're travelling to is a good idea, even if it's just to be able to go out for a walk nearby.
If you're flying long haul, especially if you're going to somewhere like Australia, make sure you build in enough time to recover from jet lag and to deal with the time difference. For example, when I was doing work in Australia, I'd fly out on Friday evening, which meant arriving on Sunday morning (because of the time difference). Ideally then I'd aim to start work on Tuesday, if I could.
Above all, although it probably seems intimidating to you right now, aim to enjoy it! I got to go to some great places that I'd never have been to if I was travelling for leisure reasons.