I don't know what kind of perennials you have- find out what growing zone you are in and that will help you a lot- but there really are just a few key tips to get you started:
1. Feed the soil in the spring and fall. It's either spend all season trying to feed the plants, or just feed the soil and let it feed the plants. You can get soil test kits that telly you about the condition of your soil, and then it's just about looking up what kinds of plants you have to see what levels they want. If something is "off," you can feed the one deficiency directly. Too much fertilizers will burn your plants so check your levels. Most areas will have a farm bureau/agricultural office/local state government gardening techs. If you look them up you can often get all kinds of information and even free soil test kits because they promote gardening!
2. Water periodically. The surface soil doesn't have to be wet all the time. What you want to do is dig your fingers into the earth. If there's moisture below the first inch or two, you don't have to oversoak. If it's dry and crumbly all the way down, give it a good soak. That means you water until it starts to pool up a little, then move to the next area. In hot summers (90+) you may have to do this two or three times a week if it's not raining. It really helps to get a good rain gauge to have in your garden. If you look up your plants it will tell you how much rainfall they like to have, so if you have a rain gauge you can just do the math to see if you need more water! If your area lets you install a rain barrel, I highly suggest you do to conserve water and cut your water bills. They are gravity fed with a hose at the bottom so you can siphon the water out.
3. Trimming encourages blooming in perennials if done correctly. Again look up the plants to see when and how much to trim. Generally speaking you want to cut some things back in the fall when they start to whither. You also will want to get some kind of mulch to cover your garden in the fall to protect it. You can save some money here - towards the end of the season if you let your grass get real long for two grows in a row you can get a big heap of tall, thick grass clippings and mound it around the bases of the plants. Under the snow during the winter it will keep the roots of the plant from freezing solid because the decomposing organic material creates warmth as it rots. In the spring when the snow melts, that organic matter is already mostly decomposed into rich black earth that will feed it in the spring. Not all perennials need this, so google your plants!
4. Weeds. Dun dun dun. In the spring some of your new growth can look like weeds. I know I've said it a million times but do google your plants, You'll get pictures of what the new growth looks like so you know what is weed and what is garden plant! If you have some open areas that are weeding concerns, I suggest planting a native breed of a hearty day lily that bushes, or something like iris. They will spread themselves so voraciously that at some point you will probably have to pull some of the bulbs or they will take over! The advantage is that they choke out the weeds. Wherever you have a thick patch of day lily or iris, you probably won't have to weed. Another fun idea for your back garden patches if this is your permanent home is to plant perennial foods that will keep providing for you. Two great ones for this are asparagus and rhubarb. Both take about three years to grow before they are ready to be harvested to eat, but once they establish themselves you will have plenty of both. Both like to be in the sun. The asparagus comes in during the mild spring and early summer. The rhubarb is good all year - note that the leaves are poisonous, you just eat the thick red stems. Chopped up and simmered with a bit of sugar and gelatin it makes an incredible topping for ice cream. Or mix it with cut strawberries and some gelatin for an OMGamazing strawberry-rhubarb pie, one of the best things there is. You can also just chop it up and freeze it wrapped tightly in bags and put it up for later use in pies and etc. Yummo.
5. Pests! Bleh! Some varieties of plant are very susceptible to diseases and pests, like soil molds that get hollyhocks and tomatos and potato beetles! There are organic and inorganic ways to address this. Unfortunately if you get soil molds, it's usually all but impossible to get rid of, and you have to just tear out the diseased plants *burn them don't turn them under you'll make it worse!!* and put in something different that's resistant. This is where your soil test kits can really help!!!
---> I'll make one safety note here...not all fertilizers and soil-feeds or treatments are appropriate for edible plants. If you want to eat from your garden, you have to adjust what you are putting in it and how you address pests. But that's all easily look-uppable.
My grandma taught me everything she knows and I'm known as a bit of a green thumb. Any veeners can always feel free to message me with gardening questions, edible plants or no! But truth be told, if you know the basics of the five tips I just gave you and are willing to go to the agricultural office folks and/or the internet when you have a problem, you should be right as rain. As a last piece of advice, MOST community colleges will have a basic gardening course, which I HIGHLY HIGHLY HIGHLY suggest you take. They are almost always taught by a master gardener who will give you all kinds of INVALUABLE information about your local growing conditions and who stays current on all the latest agricultural and farm tech progress. Find the master gardeners in your area and you will never run out of answers!
Above all...enjoy it. Gardening allowed me to connect to my grandmother in a way that makes my connection to her spirit inseparable even after her death. She is still with me - in every patch of earth and every bloom. I ate the food she grew. She is in my blood and bones. Recently her house was sold to people who grew up in the area and remember driving past her beautiful gardens. Gardening connects you to people. Take advantage of that and a new beautiful world will open up to you, where the goodness of people shows through. It's a beautiful and life enriching hobby that has added to my life beyond measure.