A lot of this is more labor than anything else.
1. Sprinkler. Right now, it's winterized. Don't dewinterize it. Why? Because if you run it, you're paying for water. $$$. And water waste. Plus, the more water the grass gets the more it grows, so the more you need to mow it. Don't water it. If it goes dormant, who cares? That's what rain is for.
2. Fertilize - you don't need to do much. A lot of people over fertilize, which wastes money and is bad for the environment. It's pretty easy though. Get a spreader (used if possible, they're expensive), get however many bags you need of the basic spring fertilizer, read the bag to determine how to set the spreader, dump fertilizer in the spreader and walk the yard. Repeat in the fall with the basic winterizer. You're done. Tip: if you get weed and feed, it'll help with weeds.
3. Replace mulch - hard labor. Rake/shovel out the old stuff, dump in new stuff. You need mulch, a rake, a shovel, and a wheelbarrow or similar. And lots and lots of water (for you).
4. Aerate the grass - plenty of people don't do this. If you decide to do it, rent the machine and walk the yard with it.
5. Leaf clean up in the fall - a mulching lawnmower that bags is awesome for this. Just rake all the leaves onto the grass, then mow! Empty the bag into whatever your local trash pickup requires - if you're lucky you can just dump it in a yard waste bin. Or 3. Otherwise, giant paper bags.
6. Weeding. Keep up with it or it'll get out of control and take 10x longer.
7. Edging. Periodically you need to edge the grass where it's up against concrete. This makes it a nice clean line. If you have an edger that helps, but it's still hard labor.
8. Mowing. Get a lawnmower appropriate for the size and characteristics of your yard. Buy it used if at all possible, they're expensive. There are probably various posts on here about different ones. They're small engines, if you're at all handy you can figure out how to do basic maintenance (I need to learn how to change the oil this spring. I may provide the neighbors some amusement, but I'll figure it out). You tube is awesome.
9. Growing grass. If you have bare spots, you can put grass seed down to get rid of them. Spring or fall is the best time, because there's plenty of rain to help it get started.
Here's the thing though. .75 acres is a pretty large yard. Maybe not big for the people who live in the country and have 2-3+ acres, but that's still a lot. You're going to spend a lot of time, and a lot of labor. You will be in much better shape. You can do SOOOOO much more, and spend endless amounts of money and time, or you can really keep it pretty basic and it'll work out just fine. I tend towards the minimalist approach, and my yard looks fine.
Full disclosure: my yard actually has a lot of issues, but I didn't do them, I bought it like that. I'm working on it. The giant bare spot in the back yard was not me. I'll get around to that one eventually, but you can't see it from the street so I don't care as much.