As a wizard:
-Look at your current job level. If you just changed, this would be 1. If you've gotten a few skills, it might be more than 1.
-Subtract 1 from it. If you just changed, that leaves you with 0. Thus, you cannot get any wizard skills yet.
-In your skills window, spend skill points until you have exactly the number you found above left (for example, if your job level is 24, spend skill points on mage skills only until you have 23 skill points left). Now the rest of those skill points may be used for either wizard or mage skills.
In other words, you can use points you earn as a wizard for either mage or wizard skills, but you may only use points earned as a mage for mage skills.