Путь: road, rails, path, way, route
It's a road! It's a path! No, it's super word: путь!
OK, so I exaggerate. But путь is one of those wonderful Russian nouns that requires a dozen English words to translate and ranges in meaning from the very concrete to the broadly metaphorical.
At the concrete end of things, путь is a road: Путь идёт вдоль реки и затем вверх в горы (The road goes along the river and then up into the mountains).
And it can mean the railroad used by trams or trains: Переходить трамвайные пути даже в разрешённом месте — опасно (It's dangerous to cross the tram tracks even on the designated crosswalks.)
Or it's any kind of route, path or way, like шелковый путь (silk route).
Путь is also a kind of stand-in for a voyage, so when someone is heading off somewhere, you can wish him счастливого пути (have a good trip), or the slightly old-fashioned в добрый путь! (happy trails!)
On the metaphorical end of things, путь is a path in life or a way of doing something. Он прошёл путь от простого солдата до генерала (He worked his way up from a simple soldier to a general).
Russians love to talk about пути решения проблем (literally "ways of solving problems"), which in English are often rendered much more laconically. Глобальные проблемы современности и пути их решения might be rendered: Today's Global Problems and Possible Solutions.
There are lots of путь expressions and idioms, like нам не по пути, which means "we're not going the same way," either literally or figuratively. In a car it means "I'm not going that way." In a divorce court, it means: "It's time to split up." `
When you run into a friend unexpectedly on the street, you might exclaim: Какими путями! (What are you doing here!)
If you're in business and your strongest competitor in widget production has just gone bankrupt, you can rub your hands together and shout: Путь свободен! (Smooth sailing ahead; literally "the path is free").
When you've either messed up or taken a career detour, you can say: Сошёл с пути (I got side-tracked, I went off base).
But if you are moving in the right direction, you can announce: Я на пути (I'm on my way!).
Путь is used in the instrumental case путём to describe the way something is done: мы решили проблему легальным/мирным путём (We resolved the problem legally/peacefully). Всё путём is a nice philosophy of life.
It can mean doing things properly, the way they should be done: Мы с невестой решили венчаться. Всё путём! (My fiancee and I have decided to have a church wedding — do it up right.)
Or it can just be a slangy way of saying that things are going great: Как дела? Всё путём! (How are things? Fabulous!)
Путевой is the adjective from путь and refers to anything related to a trip or road, like путевые расходы (travel expenses). The variant путёвый is slang for something cool or fabulous, like путёвый парень (cool guy). The negative form, непутёвый, is said of someone who is a goof-off or screw-up. Не знаю, что делать — дочь выходит замуж за такого непутёвого парня! (I don't know what to do — my daughter is engaged to such a bum!)
But you never know: пути господни неисповедимы (God moves in mysterious ways).