Ah, Spring, only days away. Anticipating longer rides and trading back up to better road bike from snow beater. Finally fixed flats recently mentioned. Don't mind divulging that reinstalling rubber is a satisfying pastime best done at home or shop rather than in field. New tires and tubes smell curiously acrid and tactilely please, whereas old are musty and worn smooth. The more care you take, the more confidence you have you'll not have to bother again soon. Although the more often one must the more proficient one gets, prefer each year to repeat just once preseason.
Potential failure modes abound, so diagnosing flats is more than just assuming a puncture. Experienced everything from side wall blowouts to valve failures. It's helpful to have a big bucket of water to locate puncture from bubbles, but indoors you can pump up tire and pass it close to your face, then likely feel air leak. Pay special attention to where puncture occurred, because there you might find glass, metal or wire still embedded, which will cause another flat. If reusing, rub entire tire through your thumbs, because you might discover multiple offenders. It's a jungle out there. Always remember, as Murphy said, if it can go wrong it probably will.
When rims are bare, it's convenient to assess rim tape, which doesn't last forever but less than several seasons. If frayed or punctured, replace with new. Also swipe all rim surfaces for grit or nicks, which can be smoothed with a bit of emery cloth. Use only the best materials for tape, tire and tube; the small difference in price is well worth it in issues prevented.
Tubes can be squirrelly and willful. Some people advocate inflating tube a bit before installing, since this makes easier to handle. Manufacturers routinely warn against doing so, since it weakens walls when not confined by rim and tire. Put one side of tire on first, and pull bead into center well of rim. Inspect and wipe tubes before installing; they are not necessarily grit free or perfect, and sometimes you run into a porous batch that hardly hold air long enough for you to go flat far from ride finish. Remove valve cap and, if presta, outside knurled nut. Pinch down tire at rim valve hole, slide in tube valve, then work tube around tire making sure it doesn't get twisted anywhere in periphery. Then lever on other tire bead. Avoid pinching tube between rim and tire or rough handling. Tubes must be completely happy tucked into that confined space.
Before inflating, inspect by pinching tire side walls and watching for bits of tube caught underneath tire bead; go entirely around, especially at valve stem. Pressing down on stem, where tube tends to hang up, pushes tube deeper into tire. Screw on presta's knurled nut about half way; it's only there to stabilize pump nozzle, not secure anything. As you inflate a bit at a time, check bead seat all around; let out air if beads don't seat evenly. More of valve stem will show, so you can screw nut down more but never tighten.
Carefully reattach wheels to fork and frame. The quick release nut should only be flush, then pivot lever back to latch tightly. Cyclists debate lever's proper position, say it should face backwards to avoid the unlikely chance that something could snag on it, dump you, or loosen wheel. Prefer to lock it astride fork or frame member, so lever is less affected by carrying bike on a rack.
Now comes the fun part: Go for a short spin to make sure your repairs can be trusted. Wear a helmet.