I can be a very anxious, worry-wart kind of person, not to the point of needing medication but enough that I have had to pinpoint what pushes me to my limit and deal with it as proactively as possible. I travel solo and that seems to magnify the "what if?" thought train even more so. Some things I have learned now that I've completed 6 solo trips abroad:
Using the ATM makes me nervous--no one to watch out for me--so I get a decent amount of foreign currency before I leave home and use a belt-loop pouch. If I need to use an ATM it will be at a bank, during business hours. I have back-up cards just in case.
Train travel--arrive early enough to ensure I understand where my platform is and if in doubt, ask a conductor before boarding. Be sure I know the stop before mine so I can be ready to exit.
I've been taking 2 week trips and this is the 2nd time now that I've realized that it may be too long of a time for me to be alone, some depression sets in no matter how much fun I'm having. So, maybe 10 days might be better.
I'm naturally a planner anyway, so by the time I hit the road I've asked all the detailed questions here that will help me be ready, and with some contingency plans in place.
Don't be afraid to ask questions or for help--at the airport in Budapest Saturday morning there was an enormous, chaotic crowd, everyone confused, not sure where to line up to check-in (some airline's windows weren't open yet) and I began to suspect I was in the wrong line, so I went right up to a clerk and confirmed that I was indeed in the wrong line. If I hadn't, I'd have maybe missed my plane.
As for eating in restaurants, I admit that while I handle it just fine, I do get tired of being alone in a sea of couples and families and friends having a good time. I tend to be ready for a meal around 4 or 5 pm, which is a bit early most places and that doesn't feel as overwhelming, more peaceful, really. I've never had trouble communicating with a waiter, and never received any surprising food.
What really helps is keeping a positive mind-set, telling myself things like "You learn by doing" and "It will be fine. It's always turned out fine, and if it's not going to be fine you will figure out what to do."