The Qur’an does not command or encourage slavery, but it accepts it as an existing institution in 7th-century Arabia and heavily regulates it while strongly pushing for the freeing of slaves as one of the highest acts of piety.

Here is exactly what the Qur’an says on the three points you asked:1. Advice / commands directed to slavesThe Qur’an gives very little direct instruction to slaves themselves, but what it does say is clear:

Verse	Text (approximate Sahih International translation)	What it commands slaves to do
24:33 (Sūrat an-Nūr)	“…And those who seek a contract [of emancipation] from among those whom your right hands possess – then make a contract with them if you know there is within them goodness…”	Slaves are encouraged to actively seek a written contract of manumission (mukātaba)
No verse	–	There is no verse that tells slaves “obey your master in everything” or “submit unconditionally” (unlike some New Testament passages).

In short: the only direct “advice” to slaves in the Qur’an is to seek their freedom through a mukātaba contract.2. How slaves earn or obtain freedom according to the Qur’anThe Qur’an mentions five explicit paths to freedom (all strongly encouraged or commanded):

Path	Verse(s)	Details
Mukātaba (written emancipation contract)	24:33	Slave and master agree on a payment or service; master is commanded to accept if the slave is capable and to help with money from zakat/charity
Direct manumission as expiation for sins	4:92, 5:89, 58:3	Freeing a slave is the penalty for accidental manslaughter, breaking a vow, or ẓihār (a pre-Islamic form of divorce)
Freeing slaves as the best use of charity	2:177, 90:13	“Righteousness is… freeing of slaves” – listed alongside feeding orphans, etc.
Zakat (obligatory charity) funds may be used to buy freedom	9:60	One of the eight categories of zakat recipients is “those in bondage” (في الرقاب fi-r-riqāb) – i.e., to purchase and free slaves
Simple voluntary manumission	2:177, 24:33, 90:12–13	Repeatedly praised as one of the steepest (and most rewarding) paths of righteousness

The Qur’an never says a slave must remain a slave; instead it makes emancipation a major religious virtue.3. Do slaves have to submit to / obey their masters?

• No verse in the Qur’an commands slaves to obey their masters in the way the New Testament does (e.g., Ephesians 6:5, Colossians 3:22).
• The only related command is directed at masters:
  4:36 – “Worship Allah… and do good to… and those whom your right hands possess (i.e., slaves).”
• Hadith literature (not the Qur’an) contains sayings such as “Your slaves are your brothers; Allah has placed them under your hands, so feed them from what you eat…” (Bukhari 30, Muslim 1661), and “Whoever beats his slave… his expiation is to free him.”
  But again, that is Hadith, not Qur’an.

Bottom-line summary of the Qur’an’s stance (not later Islamic law)

Question	Qur’anic answer
Advice to slaves?	Seek a written contract of freedom (mukātaba) if you can (24:33)
How do they gain freedom?	Mukātaba contract, expiation of owner’s sins, zakat funds, or voluntary manumission – all strongly encouraged
Must they submit/obey masters?	The Qur’an never commands slaves to obey masters; it repeatedly commands masters to treat slaves well and free them

In practice, classical Islamic law (fiqh) kept slavery legal for centuries and added many more rules, but the Qur’an itself is overwhelmingly pro-emancipation and gives slaves a clear, divinely endorsed path to freedom.