(Note of explanation: "1666||1681" means that a term was, according to the 2nd edition of the Oxford English Dictionary, first recorded in nautical use in 1666 and in general use in 1681. The average lag between first nautical appearance and first general use is more than 100 years, but, as that includes some odd cases with very long gaps, I’d be inclined to say instead that it’s usually a matter of “a few decades.”)
Before proceeding to sea, the crew will BATTEN DOWN THE HATCHES in order to prevent flooding below decks that might cause the ship to FOUNDER (1600||1613).
A ship just leaving its moorings GETS UNDER WAY (1743||1822): way is the forward (or sometimes backward) motion of a ship. If the ship continues on its desired course, it will MAKE HEADWAY (1748||1775), the ship’s bow being called the head. (The analogous nautical term sternway never made it into popular English: we prefer progress to reversals.) A ship making a lot of headway will leave a slower one in its WAKE (1627||1806), the track it leaves in the sea.
A ship that sails well BY AND LARGE (1669||1706) sails well into (by) the wind as well as with a following (large) wind, that is, under most conditions. A ship that sails really well by the wind can stay ALOOF (1532||1583) from (upwind of) other vessels. It will sail best if it is nearly ON AN EVEN KEEL, drawing the same depth of water along its whole length, rather than being much deeper at the bow or the stern.
To FORGE AHEAD (1769||1861), to proceed with effort and determination, probably comes from a common Mediterranean nautical expression meaning "to press ahead by force of oars or sail" (cf. Italian forza di remo/di vela).
To FATHOM meant originally to measure the water’s depth by the fathom (6 feet), roughly the span of a man’s outstretched arms, and later to understand the depth of a subject. Failure to watch the depth carefully might leave the ship HARD AND FAST (1867||1867) aground, and perhaps even HIGH AND DRY (1822||1838) when the tide goes out.
A ship may wait IN THE OFFING (1627||1779), or off-shore, if it is inconvenient or dangerous to approach the coast. At night or in unfavorable weather (to WEATHER A STORM), a ship might stand ON AND OFF the coast, that is, take a zigzag course alternately toward and away from the coast, giving the dangerous shore a WIDE BERTH (1829||1829) and assuring adequate LEEWAY (1669||1827), or room to maneuver, if the wind starts to blow the ship toward the lee shore. Jogging on and off requires the ship to make a leg in one direction and then TAKE A DIFFERENT TACK, a course different with respect to the direction of the wind.
Masts and other spars and rigging may GO BY THE BOARD (1630||1859), or GO OVERBOARD, by an accident at sea. "By the board" now refers to something no longer in effect: “Those regulations have gone by the board.”
The main-mast might go by the board if the enemy—like a FIRST-RATE (1666||1681) man-of-war of 100 guns, firing a BROADSIDE (1597||1833) that raked the ship FROM STEM TO STERN (1627||1842)—shot away the MAIN-STAY (1485||1787, Thomas Jefferson). The main-stay is the heavy rope leading down and forward that supports the main-mast. It might be necessary to JURY-RIG a spare mast, that is, set it up temporarily until the ship could reach a port where proper repairs could be made.
In rigging, it won’t do to use JUNK (1485||1842), old or inferior rope. The word probably comes from Old French "jonc," a rope made of rushes (such a rope being weak and inferior); compare with jonquil, a plant with leaves shaped like those of the rush.
Damage to ship or cargo is legally called AVERAGE (1491||1735), which is derived ultimately from an Arabic word for damaged goods. The damages had to be distributed equitably, or averaged, among those owning interests in the ship or cargo.
Maneuvering in CLOSE QUARTERS (1753||1809), one ship might easily RUN AFOUL (1809||1824) of another. FENDERS (1626||1919, U.S.), made of such things as old rope, serve to protect a ship during contact with a dock or another ship.
The pilot will SEE HOW THE LAND LIES (1700||1809) and use LANDMARKS (1570||1667)— distinctive features on shore—to keep the ship in the designated channel, or FAIRWAY (1854||1910, in golfing), and STEER CLEAR of obstructions. (In poor visibility, as in rainy or HAZY (1615||1665) weather, the pilot might LOSE HIS BEARINGS.)
A river-boat might HIT A SNAG (1804, Lewis and Clark||1829), which is an old tree-trunk or branch forming a dangerous obstruction.
If the ship finds a SAFE BERTH (safe anchorage), it can ride securely by its CABLE, the heavy rope used specifically for anchoring. If the crew lets nearly all the cable run out while anchoring, the rope will come to its BITTER END (1627||1849). (A bitter is a turn of the cable around the mooring bitts at the ship’s bow.) If the captain believes his anchored ship in imminent danger from the weather or an enemy, he may give the order to CUT AND RUN (1704||1861).
After receiving a CLEAN BILL OF HEALTH from the port authorities, the crew might RUMMAGE (1544||1616) the hold, removing cargo for drying or for more efficient stowing, as we might nowadays “rummage around” in the attic. Rummage later came to refer to a thorough search of a ship's holds, as by a customs inspector. A RUMMAGE SALE (1858||1890) was a sale of confiscated or unclaimed freight.
OVERHAUL (1626||1705) originally meant to pull apart the blocks of a tackle to slacken a rope, and then, by extension, to pull anything apart for inspection and repair. One might overhaul a block-and-tackle that was CHOCK-A-BLOCK (1840, U.S.||1850, U.S.), that is, whose blocks were tight against one another.
The captain may TIDE his ship OVER (1627||1821), proceeding upriver with the incoming tide and anchoring during the EBB (1000||1420), or receding, tide. (“Lunch isn’t much, but it'll tide you over till supper: I trust your appetite won’t ebb.”) He may also BACK AND FILL (1777||1854, U.S.) the ship in confined waters by letting a favorable tide carry it along more or less crosswise while alternately filling the sails to go a short distance ahead and backing the sails to go a little astern. If too strong a gust of wind strikes the ship head on, the sails will be suddenly and unexpectedly TAKEN ABACK (1754||1840), a startling situation that may result in serious damage to spars and rigging.
Sailors and GALOOTS (1812||1866)— sailor-slang for "soldier, marine" — that were told to STAND BY awaiting orders might gather briefly around the SCUTTLEBUTT (1805||1901, U.S.) for a drink of water and some gossip. The water butt, or barrel, has a scuttle cut in it through which drinking-water is dipped out. A ship may be sunk intentionally, or SCUTTLED (1642||1888), by cutting a similar hole in the hull to flood it.
A sailor who drinks too much grog, the standard navy-issue watered rum, is GROGGY (1770||1832), or even THREE SHEETS TO THE WIND (??||1821), staggering as might a ship whose sails weren’t properly trimmed (taut). A ship with well trimmed sails is a TIGHT SHIP (1971||1972, U.S.) Caution: tight also has the much older  nautical meaning "water-tight.")
Batchelder, S., Some sea terms in land speech: New England Quarterly, 1929
Manwayring, H., The Sea-mans Dictionary, 1644
O’Scanlan, T., Diccionario Marítimo, 1831; has an interesting English word-list
Oxford English Dictionary, 2nd edition
Smith, Capt. John, An Accidence..Necessary for all Young Sea-men, 1626