Flats are a huge pain in the ass. With practice you can get used to changing a tube in a few minutes but it's never fun and kind of kills your workout.

Here are a few tips. For training rides use thicker tubes and puncture resistant tires such as Continental Gatorskin; they will slow you down a little but when riding for exercise that doesn't matter. Don't try to patch a tube in the field; carry a spare tube as a replacement and then maybe patch the puncture later when you get home. Carry a pair of disposable gloves to keep the grime off your hands. Use CO2 inflator cartridges instead of struggling with a portable air pump.

I know some cyclists like self-sealing tubeless tires now. Those may work well for road racing or mountain biking, but they're not great for road training rides. I've had friends get stranded several times because the sealant didn't work as advertised.