I would limit my activity this year to watering and mowing, and possibly weeding, if you feel confident you can identify weeds. If there is a possibility you'll start pulling things out you might regret pulling, do the research first. You can post pics in several garden web forums (e.g. Winter sowing, perennials, etc) and people will tell you what it is. Give it a year and see what you like and don't like, and catalog everything you have and where it is. When stuff finishes blooming, cut down as appropriate for the plant to keep things tidy. Googling a plant name will give you lots of hits as to how to care for stuff. I would bet that a bachmann's design is filled with a lot of pretty hardy, minimal care perennials. Also I would bet that there will be an odd number of just about everything, planted equal distances apart. That will help with distinguishing weeds.

Look around to find the gardeners in your neighborhood and introduce yourself. Gardeners love to share their gardens and advice with others. It's is fun to talk/share plants and to tour each other's gardens often to see what is blooming today or how that new plant is growing.

Many perennials die back to the ground in MN so need to be cut back in the fall or spring to make room for new growth in the spring. Others may not die all the way to the ground and will only need to have dead parts cut back next spring.

Did the previous owners leave a map of the garden? If so, your plants will already be identified. spartangardener's advice to Google the plants will give you information on how to care for them. There are also many different forums on GWeb to visit and read and post, ie: Perennials, Cottage Gardens, Name this Plant, etc. They are more active than the MN forum.

Another way to have a plant identified is to take a photo or a part of the plant to a nursery. They should be able to tell you what plant you have and how to care for it.

When I move to a new home I take a year to experience what is in the garden before digging plants up or adding new ones as there can be surprises. Some plants (bleeding heart, naked ladies, oriental poppies, bulbs) will grow in the spring and die back when it gets hot to return either in the fall or next spring. You don't want to dig them up when planting something new. If you see that happening be sure to mark the spot. Also some plants come up very late (balloon flower, hibiscus) so you don't want to plant something else on top of them next spring.
If you don't have a map/graph of your gardens you may want to make one yourself. Or keep a garden journal which can be as extensive as you wish but note what is blooming, how plants are growing, what needs changing, changes you made, etc.

July is the beginning of garden tours. Look in this week's Star Tribune for garden tour information and go on a tour or two. Some are free if cost is a factor.

Visit the MN Arboretum and take along a camera and notebook. Most of their plants are marked.

Take classes, some are an hour or two and free from nurseries, local gardening clubs, the Arb.

Also come to our fall plant swap to meet other MN gardeners.
I am hosting this fall and will post information around the end of August.

Welcome to the joys of MN gardening.

Congrats to moving to Minnesota. Hopefully everything at the home looks great with the frequent rain we have had! If you have any questions or would like help in managing maintence on your property feel free to give us a call at Ground One here in Bloomington,MN.

Do take note of the sun movement and number of hours it shines where.

This is a great web site place to learn.

Check out community ed classes and metro blooms

Here is a link that might be useful: metro blooms

Thank you all SO much for the replies! (Sorry for my slow "thank you"...been very busy with the new house). Mowed the lawn once so far (THAT was interesting) and am trying to learn as much as possible about what's growing out there. There's a huge Hosta garden and lots of flowers I am still figuring out. Will take all your advise...look into the places you recommend....and keep posting questions here and trying to learn! :)