There are some chord progressions that are very common. You see them mostly in Bach music and 50's ballads. In order to show a chord progression that can be transposed to any key, one must represent each degree of the scale with a roman numeral. The tonic will be rep resented with I, etc. and the seventh scale degree with vii*. What makes the numerals upper-case, lower-case, or lower case and *'ed is what type of chord is being used. Upper-case means Major chord. Lower-case means Minor chord. Lower-case and * means Diminished.
Typical chord progression
I -> vi -> ii or IV -> V or vii* -> I -> ...
In the key of C the progression is as follows. C-> Am -> Dm or F -> G or B dim -> C...
This progression already has options, but gets boring fast. Luckily, there is room for improvement within a chord progression to give yourself more options. For instance, depending on the other instruments parts, you can put any chord that sounds good between the C and Am. The only necessary part of any chord progression is an end. I mean lets be honest, to song has to end some time. The end of a chord progression us called a cadence. There are a few common cadences that most progressions end with. One is V -> I or G to C. Another is vii*-> I, or B dim to C. Another that is common in church hymns is IV -> I, or F to C.
But, some music written in the last 100 years has used different types of chord progressions that are ruled by, usually mathematical principles.

Hope that helped you formulate progressions faster!

Also, there are things called secondary dominants, which you can google, I'm just feeling lazy, and don't want to explain them now...