I. at, on

at a time: at dawn, at six, at midnight, at 4:50

at an age: at sixteen/at the age of sixteen

• She got married at seventeen.

on a day/date: on Monday, on 4 July, on Christmas Day

Exceptions: at night, at Christmas/at Easter (the period, not the day only)

on the morning/afternoon/evening/night of a certain date:

• They arrived on the morning of the seventh.

It is also, of course, possible to say: this/next Monday etc., any Monday, next Monday.

II. by, before

by a time/date/period = at that time or before/not later than that date. It often implies 'before that time/date':

• The show starts at 6:30, so you had better be at the theater by 6:20.

before can be preposition, conjunction or adverb:

• Before signing this... (preposition)
• Before you sign this... (conjunction)
• I've seen him somewhere before. (adverb)

III. on time, in time, in good time (for)

on time = at the time arranged, not before, not after:

• The 7:30 train left on time.

in time/in time for + noun = not late; in good time (for) = with a comfortable margin:

• Passengers should be in time for their train.
• I arrived at the concert hall in good time (for the concert). (Perhaps the concert began at 7:30 and I arrived at 7:15).

IV. at the beginning/end, in the beginning/end, at first, at last

at the beginning (of)/at the end (of) = literally at the beginning/end:

• At the beginning of the book there is often a table of contents.
• At the end there may be an index.

In the beginning/at first = in the early stages; it implies that later on there was a change:

• In the beginning/At first, we used hand tools. Later we had machines.

In the end/at last = eventually/after some time:

• At first, he opposed the marriage, but in the end he gave his consent.

V. to, till/until

To can be used of time and place; till/until of time only.

If we have from, we can use to or till/until:

• The mechanic worked from 8 to 12 (from 8 till/until 12).

But if we don't have from, we can use only till/until, not to:

• We started painting the room in the morning, and worked till/until dark. (it is not correct to use to here).

Till/until is often used with negative verbs to emphasize lateness:

• The party was not over till/until 1 a.m.
• I usually get paid on the first Friday of the month, but last month I wasn't paid till/until the second Friday.

Till/until is very often used as a conjunction of time:

• We watched the movie till/until it wa over.
• Go on till/until you come to the tall buidling on the right.

But! If "you come to" is omitted, to must be used instead of till/until:

• Go on to the tall building on the right.