Lap Steel guitars as the name suggests are designed to be played sitting down, resting across your legs.
For the right handed player, the slide is held in the left hand, while the right hand picks the strings, using either fingers, finger picks or a plectrum.
The slide is used to move along the strings playing chords or notes. The slide is held as shown in the picture below. The back of the hand is used to rest against the strings behind the slide. This damps any vibrations behind the bar, producing a more defined sound.
Left Hand slide and right hand finger picking
Using a plectrum and fingers
A top view of the left hand