The laser sight pickup first appeared in Tomb Raider IV The Last Revelation. It can be combined with Revolver, Crossbow and - in the later Tomb Raider Chronicles - the Desert Eagle.
In the games it actually works more like a zooming optical sight - there is a red dot but it is within a cross-hair, and can be zoomed in or out like a rifle scope. It is the only way to aim a weapon when not targeting an enemy, or to shoot an enemy beyond the range (where Lara will auto-aim at it).
To combine it with one of the three compatible weapons, enter the Inventory and choose combine when any compatible weapon or the lasersight itself is marked.
Draw the combined weapon and press the Look Button to look through the lasersight. You can zoom in by pressing the Crouch Button, while still holding Look. Zoom out by pressing the Sprint Button while still holding Look.
The combined weapon can also be disassembled in order to use the lasersight with one of the other weapons.
In The Last Revelation
The lasersight is first found in Alexandria. It can be combined with the Crossbow found in the Coastal Ruins to use them at the Shooting Range. Later on Lara finds a Revolver to with the laser sight can also be attached.
In Tomb Raider Chronicles
In Tomb Raider Chronicles the lasersight is first found in Streets of Rome and can be combined with the Revolver. The HK Gun comes already equipped with laser sight.
Laser Sight Bug
There is also a bug called the Lasersight Bug, which enables Lara to use the pistols with the laser sight, instead of wasting precious ammo, by switching weapons while still pressing the Look button.