Richard Stayner was one of several children of Roger Stayner of Tarrant Gunville, Dorset.
In his youth served in the
Newfoundland fisheries trade. He joined the Parliamentary navy and served in a subordinate rank during the Civil War.
 On 22 June 1649 he was appointed commander of the
prize, "now a State's ship", though a very small one, her principal armament being two sakers (that is, six-pounders). She was specially fitted out "for surprising small pickaroons that lurk among the sands" on the Essex coast, and for convoy service in the
In August he captured the
, a small frigate, apparently one of
Prince Rupert's vessels, for which and other good services he was awarded £20 and £5 for a gold medal.
 In November 1652 he commanded the
, fitting out at
Chatham; but seems to have been moved from her in January to command the Foresight, which was one of the fleet with Blake in the battle off Portland on 18 February 1652. He was certainly with the fleet in the following April, when he signed the declaration of the sea-officers on the dissolution of the
Rump Parliament by
Oliver Cromwell, which was, in fact, a resolution "not to meddle with state affairs, but to keep foreigners from fooling us".
In the battle off the Gabbard on 2–3 June 1653, Stayner commanded the Foresight in the
white squadron under the immediate command of
William Penn, and was afterwards sent into the river in convoy of twelve disabled ships, eleven Dutch prizes, with 1,350 prisoners, and the body of Admiral
Richard Deane, which he was ordered to take to
Stayner rejoined the fleet in time to take part in the decisive battle of Scheveningen (29–31 July), and continued with it until the end of the season. In December he was strongly recommended by
George Monck for a larger ship, and in the following January was appointed to the
Plymouth, in which during the spring, until the end of the end of the
First Anglo-Dutch War, he was employed in active cruising in the North Sea, during which he made several captures, including one rich East Indiaman of eight hundred tons, having on board four chests of silver.
In July he was appointed by Blake to the
, and in September sailed for the Mediterranean with Blake, returning to England with him in October 1655. In the following February he was in command of the
Bridgwater and sailed again with Blake for Cadiz, which was kept closely blockaded.
In September, when the sea-generals with the greater part of the fleet went to
Aveiro, Stayner, then in the
Speaker, was left off Cadiz in command of a small squadron of some six or seven ships.
On 8 September he fell in with the Spanish treasure fleet which, having information from a prize that the English had left the coast, was pushing on for Cadiz in such perfect confidence that, it is said, the Spaniards supposed Stayner's ships to be fishing-vessels; yet three of Stayner's ships at least, the Speaker, Bridgwater, and
Plymouth, were each of more than nine hundred tons. Nothing could be done that night, and the next morning several of Stayner's ships had fallen to
leeward. He had only three with him, but these were the powerful ships just named; and as they were now within twelve miles of Cadiz, he judged that delay was unwise, and attacked the Spaniards about nine o'clock in morning. Of the four capital ships in the Spanish fleet, one escaped and ran for Cadiz, but struck on a rock and went to the bottom. The three others were captured, but two of them caught fire and were burnt with all their cargo and a great part of their men. The fourth remained in the possession of the English; some of the other ships also were taken. The value of the prize to the captors was estimated at about £600,000; but it was stated by the Spaniards that their loss was not less than nine million dollars, or nearly two millions sterling. The news of this tremendous blow reached England early in October. An official narrative of it was published on 4 October, and a thanksgiving service ordered to be held on the 8th in all the churches in London and Westminster.
Shortly after this Stayner returned to England with
Edward Montagu (later
Earl of Sandwich); but rejoined Blake early the next year, and took a brilliant part in the
destruction of the Spanish ships at Santa Cruz on 20 April.
Having arranged the ships with the utmost care and judgement, and those ships being supported by a considerable number of forts and batteries on shore, the Spaniards thought themselves so perfectly secure, in case of an attack, that their admiral sent Blake an open defiance. On reconnoitring the force and position of the enemy, the English admiral found it impossible to bring off the enemy's ships, though gallantry and prudence might render it possible to destroy them. Stayner was immediately detached to begin the attack, and being supported by Blake with the remainder of the fleet, the Spaniards were, in a very few hours, driven out of their ships and breast-works The former were instantly taken possession of by the English: and it being impossible to bring them off they were all set on fire and burnt to the water's edge.
The Royalist politician and historian
Edward Hyde, Earl of Clarendon eulogised this action, writing:
The whole action, was so miraculous, that all men, who knew the place, wondered that any sober men, with what courage soever endowed, would ever have undertaken it; and they could hardly persuade themselves to believe what they had done! whilst the Spaniards comforted themselves with the belief, that they were devils, and not men, who had destroyed them in such manner.
For his conduct on this occasion he was knighted by the
Lord Protector Cromwell on his return to England in the following August. During the rest of the year and during 1658 he commanded in the Downs, nominally as second to Montagu, who was most of the time in London, and really as commander-in-chief, with his flag as rear-admiral sometimes in the Essex, sometimes in the London, and towards the end of the time in the Speaker. His work was entirely administrative, and he had no active share in the battles of
Dunkirk, though he was in constant communication with Sir
William Goodsonn, by whom they were entirely conducted. In the summer of 1659 he was rear-admiral of the fleet with Montagu in the Sound, and on 16 April 1660 was appointed by Montagu to be rear-admiral of the fleet which went over to bring King Charles II to England. For this service he was knighted on 24 September (his earlier knighthood, conferred by Cromwell, not being recognised by the Royalists).
In the early summer of 1661 Stayner was again commander-in-chief in the Downs, and in June sailed for Lisbon and the Mediterranean as rear-admiral of the fleet under Montagu now the Earl of Sandwich. When Sandwich took de facto possession of
Tangier, it was Stayner who was put in command of the first shore battalion of seamen.
 Then, when Sandwich went to Lisbon to take
Catherine of Braganza to London, Stayner, with his flag in the Mary, remained as vice-admiral of the fleet under Sir
John Lawson. On 2 July it was reported from Lisbon that he had just arrived from Tangiers; on 20 July that he was dangerously ill; on 9 October that he had died—apparently a few days before. In pursuance of his wish to be buried beside his wife, who seems to have died in 1658, his body was embalmed and brought home in the Mary, which arrived at
Spithead on 3 November.