sirm's video guide has got you covered for 99.9% of the run. These are just a couple of quick additions.

General

If you are playing on ScummVM, make sure V-Sync is turned OFF in the graphics options. With V-Sync on the game's maximum speed will be capped by your monitor's refresh rate.

In case you want to go through the trouble of playing on DOSBox, the CD version is much, much slower than the Floppy one. On ScummVM there should be no difference between the two as long as the voices are turned off.

On top of using the menu to position your cursor as sirm describes, sometimes it's also useful to use PAUSE. If your cursor is already visible when you pause the game, it will stay visible during the pause and you can aim where you need to. This is especially useful when you are trying to talk to fast-moving characters. Pause the game, position the cursor, hold down the mouse button and then unpause.

When you press the button to open the menu during a screen transition, it will automatically open on the first frame of the next screen. So for example in the tunnels, it is safe to enter the door to the room with the crumbling ceiling, as long as you open the menu during the transition.

Don't forget that you can close the menu with Esc.

Specific Spots

Giving Lamb the ticket inside the factory causes him to start the tour immediately, so you have one less conversation with him.

Slightly faster way to get through the LINC terminal options when you use it for the first time in the Security building: 4220 2110 11