Everybody's method is going to be somewhat different, because they're using different footwear and other equipment (such as poles vs no poles).
Plan ahead and get information on what water levels are likely to be like given the time of year and the amount of snow this year. If a certain hike is likely to be impossible to complete safely, you want to know that and not do it.
If I know a big crossing is coming up, I start looking for one or two good sticks to use for balance. (I don't hike with trekking poles.)
If the creek is high enough or fast enough to look dangerous, I try to discipline myself to spend a significant amount of time searching around for the safest place to cross. The safest point may be 100 yards away from where the trail hits the creek, and may be invisible from the trail. The safest point is usually the widest, because the water flows most slowly there. Sometimes in 10 minutes of searching you can find a tree or rocks to get across without wading at all, or you'll see another hiker who will tell you a better place to cross.
Unclip belly band and pectoral strap so that if I fall, I won't be trapped by my pack. Make sure sleeping bag, down jacket, etc., are inside a trash bag or something.
I usually hike in running shoes. To cross a stream, I take off my socks and remove the inserts from the shoes, then put the shoes back on to protect my feet while crossing. Although river rocks are mostly smooth, a foot injury could ruin my whole trip, so I don't want to cross barefoot.
While crossing, rehearse what you have to do if you get swept off your feet. If this happens, shrug off your pack. The big risks of death are head injuries and getting trapped underwater. To reduce the chance of a head injury, try to orient yourself so you're going feet first.
After crossing, hike 10 minutes and then put the socks and inserts back in the shoes.
One of the biggest problems with hiking boots is that if you wear them for foot protection while crossing a stream, they will probably never dry out, and you'll end up destroying your feet with blisters.