We do not normally use prepositions in some common expressions.

After certain verbs
The verbs enter, discuss, marry, lack, approach and resemble are usually followed by direct objects without prepositions.

Let’s discuss your plans. (NOT Let’s discuss about your plans.)
She married a rich business man. (NOT She married with a rich business man.)
The baby resembles its father. (NOT The baby resembles to its father.)
They entered the premise without obtaining permission. (NOT They entered into the premise without obtaining permission.)

Before next, last etc.
A number of common expressions beginning this, that, next, last, one, every, each, some, any etc are used without prepositions.

See you next Sunday. (NOT See you on next Sunday.)
We met one Friday in June. (NOT We met on one Friday in June.)
We have meeting this Monday. (NOT We have meeting on this Monday.)

Before what time?
The preposition at is usually left out before what time?

What time does the train leave? (More natural than ‘At what time does the train leave?’)

Expressions containing words like height, weight, length, size, shape etc., are usually used without prepositions.

She is the same age as me. (More natural than She is of the same age as me.)
What color are her eyes? (NOT Of what color are her eyes?)

Before home
The preposition to is not used before home.

I am going home. (NOT I am going to home.)

In an informal style, at can be left out before home.

There is nobody home. (OR There is nobody at home.)