One of the most difficult things about moving abroad anywhere, is making new friends. In Germany friendship is a sacred thing, a friend is someone whom you can confide in and talk to about anything, including being critical. Anyone else is just an acquaintance. For this reason making friends in Germany can be difficult, but it is not impossible.
Having children or a couple of dogs helps too!
There are a few things that you can do:-
Learn some German, at least to a basic level, even if you just start with "Zwei Bier bitte", it makes your life easier and people do appreciate you making the effort. Just by starting a German class you can meet other people in the same boat as you.
Don't just travel between work and home, get out and about, enjoy the many art galleries, cafes, beer gardens, concerts and parks.
Get to know your neighbours, they are a wealth of information and I find that most people like to help. You should introduce yourself first though, it's tradition!
Try to make as many German friends as soon as possible as this will not only help with the language, but make you feel more settled. Get involved with activities in and out of work/school. If you have a hobby that you enjoy there is most likely a club (Verein) of like minded people somewhere. So see if you can join in.
Have patience, these things all work out eventually. You are not alone! If all else fails there are other expats around and about too. Find an English club in your area. Most English clubs in Germany are places that welcome everyone who speaks English, regardless of nationality. If you can't find one, start one. Meetup can help.