As for access, it depends on the sport and event. Sometimes you just ask (local games), sometimes you ask the club, sometimes you need accreditation through the organising body or association.
Can you tell us what type of sport you are interested in shooting?
GAA, Soccer, Rugby, car rally, cycling, indoor sports (swimming)?
Will the sport be during the day or evening (on a lit pitch)?
The above will give us an idea of what sport you are tyring to capture and the equipment needed to get the best results
If you are interested in shooting an outdoor sport look at your local clubs first, ask permission and explain to (the coach, club, etc.) what you are trying to do. Most outdoor amateur sports there will not be an issue shooting from the sideline, tryline, etc. just remember to avoid being in anyones way.
Indoor sports will be a different kettle of fish, beacuse there is usually a premium on room available.