Mining; It's Dirty Job...

     When it comes to mining as a beginner; each race has a specialized mining frigate which you can jump in relatively quickly. You should receive the skills and a bit of practice in mining during the tutorial missions. If you find that you enjoy mining you should focus on moving to a specialized mining vessel as soon as possible. Below is a basic fitting and skill plan that will allow you to pilot a simply fitted Retriever class mining barge (in less than 2 weeks with any luck).

Retriever, Simple Fit

High Slots:  2x Strip Miner I

Mid Slot:    Empty

Low Slots:  2x Expanded Cargohold II

Skills Required

• Science IV
• Mining IV
• Astrogeology IV
• Industry V
• Mining Barge III
• Hull Upgrades II

     You will notice a great improvement in your mining ability when stepping up from a mining frigate to the Retriever.  The next step from here would be a Hulk class Exhumer.
    
     However, before moving on from this point I would like to advise that any new player take some time to train their support skills, chief among these being the learning skills, followed by ship support skills.  Your learning skills will allow you to learn new (and exciting) skills much faster as you progress in EvE and will benefit you for the remainder of your career.  The ship support skills will also benefit you for a long time and will help you become better at flying every ship, including the ones you are already in.
     EVEMon will help by suggesting the learning skills that can speed up your training in the bottom lefthand corner (click on the link).  It can also help you with your ship support skills.  You may want to consider learning the first level of all the "Core" certificates under EVEMon's "Certificates" tab (right click to add to queue).