Make a photo, don’t take one. Look for a background and light that works with your subject/s. Make the most of what you’ve got available e.g. light, time, location. Using the right settings on the camera goes without saying then after that, anticipate the shot or shots you’re going to take. Look for an interesting angle, give them some direction, make sure you’re ready for what’s to come and then shoot through the action / movement / expressions.
It’s really important to work with the person / people as individuals. Not everyone feels comfortable doing the same thing / posing in the same way and not everyone relaxes at the same speed. For some people it comes naturally and others it takes while.
Be patient, talk to the subjects, put them at ease and find something that works for them. When you’ve found their ‘thing’, then the great shots will come.
For events, it’s a case of having a shot list at the start to make sure all the important parts are covered, then look around, be observant and shoot the interesting stuff. Include wide shots and close-ups for a good variety of images.