Working with Roving/Sliver/Top

Carded fibre that comes in continuous rope-like lengths goes by the names of roving, sliver or top depending on how it was prepared. If you're new to handling fibre in this form, try these tips:
breaking off a piece of roving
Firstly, check that the length of roving is straight with no twist in it. Even a little twist can make pulling it apart difficult. Next, grasp the roving in each hand with at least a staple's length gap between them. For this demonstration I'm using merino wool which has a typical staple length of 7-12cm (3-5"). If your hands are closer than a staple's length, the fibres can't begin to slide apart. Pull gently to separate off the piece you need.

splitting a piece of roving lengthwise
The way I do this is to dig my thumbs into the centre of the roving a short distance from the end, easing apart the fibres to split the end in two.

Once the end is split, pull the two halves apart down the length of the roving. Using the same method, you can split each of the two halves in half again to divide your original roving into quarters. If you're working with a thick roving, you can split each piece again to get eigths. For felting, these thinner divisions of roving can give you more control over how much fibre gets pulled out when laying down the fibres. Similarly for spinning, some find it easier to control how many fibres are being drafted out when working with thinner pieces of roving.

pulling off wisps of fibre for felting
For this demonstration I'm using a "quarter-split" sized piece. Using an index finger, I pin down the wispy fibres at the end. Holding the roving in my other hand, I gently pull back to separate out a fine layer of fibre.

To pull out a thicker layer of fibre, you can pin down more fibres before pulling back. Experiment and find what works for you :)