If inflating a number of balloons, lung power may not be the best option -- unless you have a number of friends to help out. Instead, opt for helium balloon tanks or balloon pumps to inflate those balloons fully and safely. If you do wish to inflate the balloons manually, stretch them or preinflate them with a pump.
When blowing up a balloon the old-fashioned way -- using air from your lungs -- stretch the balloon a few times to loosen up the latex a bit, making it easier to inflate to its full potential size. Stretch the balloon vertically and horizontally, and then blow it up by mouth.
Take a large breath, then exhale into the balloon long and steady, letting the air out of your lungs. Use your diaphragm and chest to force the air into the balloon once the balloon starts to inflate. If the balloon is difficult to inflate from the start, fill your cheeks with air and use that air reserve to force the balloon to inflate.
Manual and Mechanical Pumps
A manual balloon pump works similar to a hand-operated bicycle pump, filling balloons with air without requiring lung power. A mechanical balloon pump is like an air compressor, requiring electricity to inflate the balloon. In either case, hold the mouth of the balloon over the pump nozzle, and then fill the balloon until it is full, but not over inflated. If regular balloons take on an extreme pear shape, it may be over inflated. Let a small amount of air out, and then tie the balloon closed. A manual pump is best if you're inflating a dozen or less balloons; any more than that and a mechanical pump may be worth renting or purchasing.
Preinflate balloons with a manual or mechanical pump, allowing the air to escape afterwards, to make the balloons inflate quickly and easily by lung power. Inflating them to full size stretches them out enough so that they remain slightly stretched when you need to inflate them the old-fashioned way. This technique comes in handy if you wish to impress friends or guests with your ability to blow up balloons quickly.
If your goal is for the balloons to float, a helium tank is a necessity. Rent or purchase a helium balloon tank to fill the balloons, keeping in mind that metallic foil balloons do not stretch like latex balloons -- they won't get much wider or taller than they look when deflated. Use latex balloons designed to be inflated to a large size, if size is the goal -- otherwise they may pop.
Oh So Simple
If your main goal is to inflate balloons to as large a size as possible, purchase huge latex balloons from a party supply shop, rather than standard bagged balloons available just about anywhere. All latex balloons have a breaking point; if a balloon is designed to have an 18-inch diameter, don't blow it up beyond that or it may pop.
Do not over-inflate balloons to see how large they can get. They will pop and could cause injury.