Mechanical Designers typically use CAD software to generate designs either in 2D or 3D. Generally 2D is used to show outlines of a design with dimensions on for manufacturing. 3D designs are used more for automated machining where tolerances are not that important (although an overall tolerance to the design can be allocated).
It is a mechanical designers job to design machines and products using new technologies available. With technology changing constantly and the introduction of new products its the mechanical designers job to constantly look for new and improved solutions when designing.
Dependent on which industry the mechanical designer is in it is their job to understand industry standards on what they can and cant do. The responsibility of a mechanical designer is very high when designing as any mistakes could cause fatal accidents or loss of money.
A mechanical designer should know how to use drafting software and understand how limit tolerancing techniques, or geometric dimensioning and tolerancing.
Typically to become a mechanical designer you need to study for four years and even longer if they want to become licensed.