Generally, lancers were used exactly as you would expect them to, to smash unprepared troops and to pursue routed troops. Generally scouting would be preformed by light cavalry which included lancers but in the French Army, that would be the main job of the Chasseurs a Cheval and the Hussars.

The Polish lancers (ulans as uhlans are the German name) showed distinction in Napoleon's 1808 campaign in Spain, where they used a sudden squall in a storm to get close and destroy a British battalion that was unaware. From this, Napoleon created nine lancer units (known as chevau-legere lanciers) from Dragoon units as well as new recruits. The Polish lancers were integrated into the Imperial Guard as the 1er Lanciers de la Garde and were allowed to dress in Polish cut French uniforms.

As for how they were used, mainly they were used as mentioned above but were intended to fight infantry squares. The lance at this time was around three meters in length and could easily spear soldiers that stood in a square. However this wasn't fully effective since the soldiers had muskets and could easily hit a horse that was a few meters away, so rarely were lancers used as they were intended.

During the Napoleonic Wars, heavy cavalry was generally armed with long, straight swords that were intended for stabbing. So cavalrymen such as the Carabineers, Cuirassiers, and the Grenadiers a Cheval de la Garde were on large, heavy horses, sometimes armored with a breast plate, armed with several pistols and a heavy sword.

I don't know in respect to Medieval warfare but lances being a weapon of heavy cavalry is more Medieval than Napoleonic.

Lancer units were in general fairly inept in close quarter combat due to the nature of the weapon. It was simply more practical to arm heavy cavalry with long, straight swords as they were still effective enough at charging into enemy units. It's for this reason that Lances fell out of use. Swords were good enough at the job of breaking enemy formations (See the aftermath of the Battle of Vauchamps) that, although not as effective as a sword in the initial charge, it was pointless to have large clunky lances that couldn't be used once close quarter combat had started.

Interestingly enough some lancer units stayed around for some time after the Napoleonic Wars. The British didn't abandon them completely after the Boer Wars and other European nations had them removed once World War I had started and it was obvious that anything but a gun was pretty much useless due to their fire power.