I've sailed a 15' sailboat on lakes.
I've learnt about sailing from the US Navy's texts.
I've been aboard a sailboat (50') underway.
I've played Wooden Ships and Iron Men, Sky Galleons of Mars, and several other very well done sets of rules with sailing.
A sail comes in one of two types: a wind catcher, and an aerofoil.
Most are actually aerofoils; the few wind catchers have typically been used to drive propellers, tho almost all can be angled to merely catch the wind.
Wind crossing the sail (at about 30-45° out from dead astern) provides the maximum thrust forward on most sailing craft, with the sails angled so that the ship is actually using the sheets as wings whose thrust is forward (essentially, a propeller). Note that this can get some ships to over 150% of wind speed (In a 10kt wind, I made 15kts speed in the water).
When the wind is blowing into the sail itself, the best designs get about 75% of windspeed, with traditional sailing vessels getting about 20%.
Forward quartering winds generally only get you 25-50% of wind speed on traditional vessels, and up to 75-100% on modern ultra high performance sailing craft.
Several non-sheet wind craft exist. One uses a trio of mast mounted vertical blades which the wind drives in circles around the mast by a gearing which is adjusted for the wind direction. These rotating blades drive a shaft, the shaft is geared to a propeller.
Another design, very poor, rather slow, is the wind paddle... which is a lightweight paddlewheel, which is then geared to a propeller. Efficiency was low, and most efficient was dead aft. I've seen one photo of one experimental. Not competitive.
A few modern designs use wind turbines to generate electrical power, and drive motors that way. More efficient transmission, less efficient conversion. About on par with mechanical linkages, from what I've read.
Currents tend to drag vessels along at between 10% and 90% of current speed. 10% if you have aimed your bow in and are low drag; 90% is not unheard of for high drag vessels side on.
Higher winds complicate matters, as the rigging can't handle the additional stress, and additionally, higher winds generate higher swells; swells may cut off stable wind, resulting in gusting and capsizing. So, in general, once winds cross (IIRC) 30-40 kts or so, most traditional craft had to furl the sails to prevent them being ripped. Modern polymer sails can be used to at least 40kts safely, and higher if designed for it... but not always, and the sea state at that point is usually too rough for the crew to work the decks. The fastest sailing vessels hit into the 50-60 kt range in ideal conditions.
That help?