For flats, I like to carry a spare tube and a small pump. Or...a spare tube and a CO2 inflator with a couple of cartridges.

On long rides I sometimes throw in a patch kit as well, in case of having two flats.

Pack along a set of tire levers too. I actually carry just one lever to save a bit of weight. Wouldn't want to be without the one though.

It's worth doing a tube change at home as a dry run, just to be sure you have the procedure down. First time I used a CO2 inflator, I ended up doing it wrong and venting all the CO2 into the atmosphere.

Do you have flat-resistant tires? Those are worth a look if you can't afford to be late to work due to fixing a flat.