Dates

In the short date format, the order of the day and month are reversed in British and US English. Therefore, when writing dates, use the longer format to avoid ambiguity, for example 4 July 1776:

British English
4‑7‑1776

US English
7‑4‑1776

Better
4 July 1776 or July 4, 1776

If you wish, you can add -st, -nd, -rd, th after the date, for example 1st, 2nd, 3rd, 4th July. However, this is not necessary. The date format with superscript 1st, 2nd, 3rd or 4th is now somewhat old-fashioned.

Years

Decades and centuries can be written without an apostrophe:

The 1900s saw great changes in many countries.
The 1960s were a time of great social change.

Unless you use the abbreviated form, in which case an apostrophe should be added before the date:

The ’60s were a time of great social change.
The ’40s saw widespread famine.

However, this abbreviated form is more informal and potentially ambiguous. In university and research writing, therefore, it is better to write years in full.

When referring to year ranges, if you abbreviate, abbreviate sensibly so that the meaning is clear.

BC and AD

Where used, BC is written after a date and AD before a date in formal writing, for example:

55 BC AD 1066
25,000 BC AD 1564

However, as BC means ‘Before Christ’ and AD is short for ‘Anno Domini’, which means ‘In the Year of the Lord’, you may prefer BCE and CE respectively as more neutral alternatives. BCE means Before the Common Era, and CE means Common Era.

Time

Beware of using relative terms, which vary depending on when your work is written or read, for example:

in the last five years
Better: from 2005–2010

next year
Better: in 2010

This is particularly the case for texts with a long time span, such as a thesis or a book.

In writing times, British English usually uses a full stop to separate hours and minutes, while US English uses a colon, for example:

7.30 (British English)
7:30 (US English)

If you use the 12-hour clock, a.m. means before noon, and p.m. means after noon:

Breakfast is served from 7 a.m. to 9 a.m.
Dinner is at 7 p.m.