I recently switched to using a mechanical pencil (recently being since last September) and these eraser shavings that seem to be everywhere are driving me crazy!
I've had a look at things like this and this, but it's hugely inefficient to keep using these to clean up the shavings every time I erase (which is quiet frequently, I'm a little picky with neatness of notes). It has also been noted that the second link actually leaves a mark when rolled over white paper which isn't pleasant at all.
Use a hard pencil (i.e. one that doesn't easily smear) and just brush off the shavings with your hand or - as has been suggested - a soft brush. Hold the paper on one side and brush away from there to avoid crinkling it.
For softer pencils you can use kneaded erasers (putty erasers) which avoids the problem in the first place. They don't work as well for harder pencils, but you can also use them to collect the shavings from a normal eraser. This is what I've always used for pencil drawings to avoid smearing.
You can collect the eraser shavings for awhile, then once you get a small pile of them, you can start to make them into a new eraser. To make the new eraser out the shavings, you will need to have your fingers slightly damp, and then start compressing the shavings together. Start with the largest shavings first and dampen your fingers again as they dry out. After a bit, they should start sticking together and you can keep adding shavings to the ball you make. It should take on a consistency similar to silly putty and be slightly sticky. You can then use the new eraser to pick up more shavings and add to it, or as an eraser. Every time you use it (on different days), you should knead it with slightly damp fingers to keep it malleable and to prevent it from hardening. It can easily pick up new shavings, and you can then reuse them.
Use a Vinyl eraser and a metal eraser guard. Use a kneaded eraser to pick up the pieces. Vinyl erasers can erase almost anything and kneaded erasers can be shaped to fit any space and they do not leave any residue behind. Also, if you use an electric eraser, this may help with the accuracy of what you are erasing.
Use a Dyson (or other high powered) handheld vacuum after your drafting session
I use my hand to brush shavings into a side or corner of the table as I'm drafting.
I don't like brushing shavings onto the floor because they get blown around or stepped on accidentally.
Eraser shavings tend to want to stick to surfaces because of the rubber compound, so high powered handheld is great at sucking every last one of them off the table at the end of the session.
Because of the (synthetic) rubber friction, the shavings aren't always easy to brush off using a drafting or dust brush, because the bristles apply some downward force onto the shavings, causing some to stick or roll slowly rather than fly smoothly into a pan. Sometimes the bristles spring forward and flick stray shavings elsewhere, where they hang out annoyingly until a wider cleaning.
It's really satisfying to see the shavings disappear into the vacuum, leaving you with a nice clean table.