TL;DR

Do assume eventual compromise of your password database (this means prepare for the worst)
Do encrypt website traffic with TLS
Do keep your servers up-to-date (especially security critical software like OpenSSL)
Do hash passwords with Argon2, Scrypt, Bcrypt or PBKDF2 and set an appropriate high work factor (bcrypt: cost >=11).
Do enforce passwords to a minimum of 8 characters (generally longer passwords are better, I prefer larger than 12)
Do rate limit authentication attempts and block repeated bad actors.
Do blacklist top used passwords (123456) / common password masks (?u?l?l?l?l?d?d) / keyboard patterns (qwerty)
Do block passwords that where in previous data breaches
Do offer Multi-factor Authentication (Avoid the use of SMS, more examples: reddit)
Do allow users to delete their accounts
Do not enforce a limited character set (allow all ASCII and Unicode characters, yes you should allow emoji as part of a password👌)
Do not enforce a maximum password length (if you need to have it, set it a reasonable high number. OWASP suggests 160 and NIST up to 64 characters)
Do not enforce the rotation of passwords
Do not block form auto-fill or pasting in the password field. Doing so unnecessarily restricts the recommended use of a password manager.

Another option is passwordless

Resources

Example of what not to do

Hash speed

1 kH/s is 1,000 (one thousand) hashes per second.
1 MH/s is 1,000,000 (one million) hashes per second.
1 GH/s is 1,000,000,000 (one billion) hashes per second.
1 TH/s is 1,000,000,000,000 (one trillion) hashes per second.
1 PH/s is 1,000,000,000,000,000 (one quadrillion) hashes per second.
1 EH/s is 1,000,000,000,000,000,000 (one quintillion) hashes per second.
Source: https://bitcoin.stackexchange.com/questions/9219/what-is-the-difference-between-kh-s-mh-s-and-gh-s#9220

My 2012 laptop can hash 284.6 Million MD5 hashes per second (284.6 MH/s).

Now the guys that hash passwords for a living:

In case you were wondering what 300 kg of @NVIDIAGeForce GPUs looks like. I love this job :) pic.twitter.com/EgPK2o00a3
— Jeremi M Gosney (@jmgosney) March 1, 2017

@vortexau @NVIDIAGeForce should be ~ 7 TH/s NTLM, 4 TH/s MD5
— Jeremi M Gosney (@jmgosney) March 2, 2017

That is 4 Trillion MD5 hashes per second. Let’s see how long it would take to retrieve passwords hashed with MD5 using brute-force:

Description	Example Password	Example Password	Duration
8 character password (lower-case letters)	slrudowq	password	about 53 milliseconds
search space / hashes per second = brute-force time in seconds 217,180,147,158 / 4,000,000,000,000 = 0.05429503679 seconds = 54.3 milliseconds
8 character password (numbers, letters)	m7wY8sDs	P4ssW0rd	about 1 minute
221,919,451,578,090 / 4,000,000,000,000 = 55.4798628945 seconds
8 character password (numbers, letters, symbols)	$QWt+4V:	P4$$W@rd	about 30 minutes
6,704,780,954,517,120 / 4,000,000,000,000 = 1,676 seconds = 27 minutes 56 seconds
10 character password (numbers, letters, symbols)	FN*vX5t8=o	P4$$W@rd10	about half a year
60,510,648,114,517,017,120 / 4,000,000,000,000 = 15,127,662 seconds = 25.01 weeks
14 character password (lower-case letters)	guxpzsvhzpizgz	passwordqwerty	about half a year
67,090,373,691,429,037,014 / 4,000,000,000,000 = 16,772,593 seconds = 27.73 weeks
12 character password (numbers, letters, symbols)	Tc0rBVK,\s]9	Tr0ub4dour&3	about 43 centuries
546,108,599,233,516,079,517,120 / 4,000,000,000,000 = 136,527,149,808.379 seconds = 225,739 weeks
28 character password (lower-case letters, symbols) 4 random words / diceware	zorn snug woke stable jockey	correct horse battery stable	really long time if using brute-force
Brute-force: 3.90x10^49 / 4,000,000,000,000 = 9.75x10^36 seconds = 3,091,704,718,417,047,290,000,000,000 centuries Diceware Dictionary: 7776 x 7776 x 7776 x 7776 x 7776 / 4,000,000,000,000 = 7,107,572.00748243 seconds = 11.75 weeks

Try it yourself at: https://www.grc.com/haystack.htm

Now most password cracking is not done with brute-force. It is done with password lists, mutations on the lists, rainbow tables and password masks. This reduces the time to guess the correct password considerably.

Tr0ub4dour&3, password, P4ssW0rd, P4$$W@rd, P4$$W@rd10 and passwordqwerty, would all take less than a second with the same set-up. But FN*vX5t8=o and guxpzsvhzpizgz are completely random so it would still take about half a year with brute-force.

Try it yourself with zxcvbn