The first thing to understand about getting things done is that you're not going to get as much done. Maybe it's not what you want to hear, but it's important that you have realistic expectations. Please let go of the expectation that your house will be spotless and you'll go back to work at 6 weeks doing exactly what you did before. Newborns take a lot of time to feed and keep clean and happy. You're also recovering from birth and adjusting to a new family member. All of this is enough! But at some point you'll need to get back to accomplishing tasks, although you won't be back to pre-birth productivity while caring for your baby (and that's ok!)
Plan it out
You may not have been organized before having a baby, but afterwards a loose schedule can really help. Without it, time tends to fly by. If you're finding there are tasks you're consistently not getting to, try planning out the time you'll do them. After the first few weeks your baby will have some semblance of a rough schedule, and you can plan the best times for different activities. Many babies have a fussy period in the evenings, so that might be time for a bath with baby or sit-down work while constantly feeding.
One of the best ways to keep a baby happy so you can do things is to wear them in a baby carrier. Babies who are worn more are shown to cry less and have better social skills since they are constantly around an adult learning more than you think. Baby won't know you're throwing a load of clothes in the dryer or packing a suitcase; all they know is you're holding them and they like it. It's also great for chasing around toddlers without worrying about leaving the baby. If you wait until baby is able to be put down to do anything you might be waiting awhile! There are many, many types and brands of carriers, and different ones will work best for different babies and different ages. My babies love their sling when newborn and an Ergo when older.
Make a "Nest"
Especially for the first months when babies seem to be eating constantly (babies should eat at least 8 times a day), consider making a "nest". In the most comfortable place in your house gather everything you'll need for feeding, changing, keeping baby happy, and some things to work on. Don't forget some snacks and drinks for you! It saves a lot of time and frustration to have everything right there when you need it. Perhaps that book you've been wanting to read for times when baby will only sleep in your arms. This nesting strategy can work well for older children when they're sick and need extra attention, too.
In the Wee Hours
One given about parenting is that you'll be up at night at least some of the time. Are there things you could do while you're awake anyway? One word of caution: The fastest way to discourage long night waking is to keep the lights and noise low, so they realize night is different than daytime. But you might listen to a podcast or lecture, do a little picking up with one hand, or do a little work on the computer while holding your awake sweetie. Sleep deprivation is a very real thing during the postpartum time, so I'm not advocating staying up if everyone else is sleeping. Work in the middle of the night is only for when baby is awake. If you're up at night I highly recommend a daytime nap with baby. A 20-minute nap can be a real life-saver!
At the risk of sounding cliché, you'll never get this time back. I doubt any 90-year-old woman wished she had spent the first months of her baby's life doing other things. Often we stress ourselves out by filling our plates with things we really don't want to be doing anyway, just because we think we have to. Try to drop the things you don't enjoy so you can have more time to spend on the things that are really important to you. Then make the drudgery more fun. Maybe throw on some music while you sweep and get some exercise in a beautiful place outdoors.
Spend a few more moments smelling that sweet head, taking pictures, or holding hands with your husband as you stare at the peacefully sleeping face. Those are the things life is all about, anyway.