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What are the criteria to determine whether a Shabbat prohibition is on the Torah (biblical) level or the rabbinic level? As a rule, for a melakha to be biblically prohibited:
It must involve taking an action which has a lasting result. Doing something which only has a temporary effect is rabbinically prohibited. For example, someone who writes with a standard pen or pencil is transgressing biblically, while someone who writes with disappearing ink is transgressing rabbinically.
It must be constructive. Destructive actions, such as tearing clothing or destroying things, are rabbinically prohibited.
It must be done in the usual way. However, the Sages put a safeguard in place and forbade doing a melakha even with a shinui (an irregular way). Why is it allowed on the Torah level? Because Shabbat demands abstaining from work. Someone who does his work with a shinui is in effect taking a break from work, because it is not viable to work this way. For example, if one normally writes, cuts, or hammers with one's right hand, but is forced to use the left instead, one will only be a tenth as productive as normal. Therefore, this is only rabbinically prohibited. Here is another example. If two people grasp a pen together and use it to write, this is a major shinui. Since it is impossible to write efficiently this way, it is prohibited only on the rabbinic level.
There is an additional principle with regard to a person who causes a melakha to be done in an irregular way and the action is indirect (grama). This transgresses a minor rabbinic prohibition, and therefore in exceptional circumstances, doing so is permitted. (For examples, see sections 20-21 below.)
