First, always be sure that you have clean, sharp clippers. Remove any old debris from your tools with warm soapy water. Using an old toothbrush is a great way to scrub old dirt and grime off. Sharpen to be sure that when you snip through a branch or stem, it is a clean, straight cut. Dull blades will mash stems, rather than cut, and that isn't good for plant.
The first type of pruning you should always do is to remove dead or damaged leaves and stems. This should be done on a regular basis. Old plant material invites insects and disease, so keeping only healthy leaves keeps plants strong and thriving. Other times to prune are if a plant has overgrown its pot, or if you just want to reshape a plant that is growing in ways that you didn't anticipate.
You'll probably find yourself trimming fast trailing growers like pothos, philodendrons, and monsteras the most. If they are happy plants, their vines will grow quickly and can overtake the space you have for them. These are also the easiest to prune. Snip the vines just below a leaf node at a level that is higher than the actual length that you want. That will give them room to grow. For fast-growing plants of this nature, sometimes they put out so much foliage that the pot you have them in can't support it all. Giving them a little hair cut and a little fertilizer will usually breathe new life into the plant overall.
For leafy plants, such as calathea and stromanthe, you'll find that you can't do a shaping prune the way you might on shrubs outdoors. When you need to prune leaves off of these plants, follow the leaf to its stem and trim the stem as low as possible without damaging the ones you are leaving. This type of pruning thins the plants out a bit, removes unattractive leaves and redirects the energy of the plant into putting out gorgeous new leaves, instead of trying to support old ones.
For taller, stemmy plants like ficus, dracaena, or money trees, you can always do a little light trimming to remove old leaves as needed, but occasionally you may have to cut whole stems or branches to reduce the overall size of the plant.
That doesn't cover every type of plant you may have, but hopefully gives you a few tips and a little confidence to go forward and prune. Remember that plants recover quickly and will often show their appreciation for pruning with a new flush of beautiful foliage. And now, with spring approaching, it is the best time of year for doing any type of pruning that is needed. Even indoor plants react to the change in seasons and have some of their best flushes of growth at this time of the year. So, don't be scared, grab your clippers, and get pruning.