If you know broadly what destinations you will be flying to, check out which airline flies to most or all of them and get yourself on their frequent flyer programme. Rack up the maximum (usable) status and reward miles with the same airline if possible, and enjoy the privileges that come with them. Ditto hotels, although if you have the choice of where to book you may want to opt for non- or smaller-chain hotels where you will probably get much better service if you are a regular guest. Do research online for good local restaurants, and try to get to know the places you visit a bit rather than just the hotel.
Always pack earplugs, adapter plugs and imodium. Take a camera. Take plenty of business cards. As others have said, pack light and carry your stuff on, don't check it. Have enough local currency in your wallet at least to get a taxi between the airport and the centre of town, in small bills. Prepare for the snafus and irritations of regular air travel - a plan B for anything serious; movies, books, music, family pics etc on your tablet or laptop; some spare ID photos (useful if your passport goes awol and needs to be replaced in a hurry); a relaxed attitude. Leave a photocopy of your passport, driving licence etc in the office. Consider investing in local SIM cards if you are going to do a lot of phoning at your destinations; roaming call charges are horrendous and data even more so, but the company may not mind this. Keep all receipts (Number One Rule)! Make sure your channels back to loved ones are all set up, and use them.
And don't forget the unappreciated worker bees back at base who never get a trip overseas on the firm. Bring back sweets or something from your trips that can be shared around the office.