Learn Turkish: Yürüyüş için yağmurluk giyecektim. - I was going to wear a raincoat for the walk.

It combines the future tense and the past tense! The root is giy- (wear). We add the future suffix -ecek, then the past tense copula -ti (was), and finally the 'I' ending -m. Together, -ecekti expresses an unfulfilled intention: 'was going to'. So giyecektim means 'I was going to wear' (but probably didn't).

How is the word yağmurluk (raincoat) formed?

It comes from yağmur (rain) plus the suffix -luk. This suffix is often used to create a noun that relates to the original word's purpose or container, like tuzluk (salt shaker) from tuz (salt). Here, it creates a wearable item meant for the rain.

I know yürümek is the verb 'to walk'. What is the -yüş at the end of yürüyüş?

The suffix -(y)iş/-(y)üş/-(y)uş/-(y)ış turns a verb into a noun that describes the act or manner of doing it. So yürü- (walk) becomes yürüyüş (a walk, or the act of walking). Another common example is giriş (entrance) from gir- (enter).

Why doesn't the Turkish sentence use bir for 'a raincoat'?