We do not use prepositions in some common expressions. In some other expressions, we can leave them out.

After discuss, enter, marry, lack, resemble and approach

Verbs like discuss, enter, marry, lack, resemble and approach are normally followed by direct objects without prepositions.

• We discussed his plans. (NOT We discussed about his plans.)
• She married an old man. (NOT She married with an old man.)
• They entered the church. (NOT They entered into the church.)
• She lacks tact. (NOT She lacks of tact.)
• He resembles a Greek God. (NOT He resembles to a Greek God.)

Before next, last etc.

Prepositions are not used before a number of expressions beginning next, last, this, that, one, every, each, some, any and all.

• See you next Sunday. (NOT …on next Sunday.)
• Come any day you like.
• We met one Friday in June.
• The party lasted all night.

Before what time…?

We usually leave out at before what time.

• What time does her train arrive? (More natural than At what
  time …)

In an informal style, at is often dropped before about + time expression.

• I will see you (at) about 5 o’clock.

Measurement expressions after be

Expressions containing words like height, weight, length, size, shape, age and colour are usually connected to the subject of the clause by the verb be, without a preposition.

• She is the same age as me.(NOT … of the same age as me.)
• What colour are her eyes? (NOT Of what colour …)
• I am the same weight as I was ten years ago. (NOT I am of the same weight ...)

Before home

We do not use to before home.

• Let us go home. (NOT … go to home.)

In informal English, at can be left out before home.

• Is anybody (at) home?