You can gain handiness skill by repairing objects that are broken or you can buy a book from the book store and read it to gain the skill like that.
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The handiness class can be taken at the Millitary, which can be found in all sims 3 towns.
The military base, Fort Gnome Military Base I think its called. :):)
If you have sims 3 ambition expansion pack you can be self employed.
You go to the hobby shop,buy a fire hydrant,place it in your home or outside of it,click it,then click "Practice Firefighting" until you gain a firefighting level.
Their is several ways. First you can go to I think its the science lab or the military base and you can click on take handiness class or you can fix things in the house or tinker with thing by clicking on them and selecting "tinker" Hope this helps!!