Months and days of the week

With the names of months and days of the week you usually use no article when you want to relate a period to the present, for example 'on Tuesday', 'in May'.

However, you can use the indefinite article with the days of the week to identify one day of the week in general.

Don't do it on a Monday.

It was always washing on a Monday and baking on a Wednesday.

Compare this with 'He bought it on Monday', meaning 'last Monday'.

You can use the definite or indefinite article with qualification or modification to refer to one particular day.

...Monday April 17, an ordinary Monday.

...not later than the second Monday in May.

A definite article without modification suggests a day in the week you are talking about.

It got under way at two o'clock on the Tuesday, having been meant to start on the previous Friday.

Parts of the day

You can use articles in the normal way when referring to a part of one particular day. You can also use the definite article when you want to stress one part as opposed to others.

The best times to take the temperature are in the first part of the morning and late in the afternoon. Traditionally cooking was carried out in the evening.

Sometimes I wake in the night in a panic.

... during the day.

Here 'day' does not refer to a 24-hour period, but only to part of one (as opposed to night); if you want to make this clear you can use 'daytime'.

...especially in the daytime.

'Night' is used after 'at' and 'by' without an article. You can also say 'by day'.

The practice of giving a baby a bottle of water at night is a bad one.

Longer periods

Words like 'day', 'week', 'month', 'year', and so on, are typically count nouns and so can be used with both the definite and indefinite articles.

...the day after the trial.

She had been there for over a year.

A week later she found a job.

Like 'day', 'week' has two meanings. It can be used to refer to a period of seven days, as above, or to the days between two weekends. The expression 'during the week' can be used to mean 'on the days between weekends'.

People used to come at the weekends, but during the week I was alone in that huge house.