In order to take sabbatical for a full year at some institutions, you have to be prepared to lose part of your paycheck. Believe me, it's totally worth it (particularly because sabbatical is giving me a break from the chaos pervading my workplace)--but you still have to pay your bills, especially if you're like me and your paycheck is the only paycheck coming into your household. In my case, I took a 35% pay cut.
So in order to fund this full year, the first step is to save up what you need to cover your expenses for the year. One of the upsides of living through a global pandemic is that we are one of the lucky families who ended up saving all the money we weren't spending because we weren't going out to eat and venturing places where the money is easy to spend, and I kept my job. So, despite not really planning to need to save up for sabbatical, I ended up stashing away enough to cover the difference in pay. Also, those extra child credit payments are basically making up a good part of the difference too. All of this is to say that I had good timing and a few other factors on my side, which may be hard to replicate, but certainly took the pressure off given that I didn't originally plan to have to cover the pay gap.
Second is to budget, budget, budget. I figured out how much my monthly income would be with the pay cut and figured out roughly how much we'd need to try to spend on things like groceries. We like good food and if left to our own devices, we end up spending more on food than is strictly necessary, so now I hound my spouse to stay under a specific number and *surprise* he does--and we still eat delicious food. This took about a month or two to get used to, but now we seem to be able to stay mostly within our budget. Also, we're still not eating out much (like maybe once a month) or buying coffee out anymore (which would be higher if I could actually go work at a coffee shop), so that amount continues to be very small. We use YNAB for our budget (link contains a referral code), and I like it a lot--it synchs with all your accounts and helps you spend only the money you have if you're also using credit cards because it makes those expenses visible, even if they aren't coming out of your bank account in the moment.
Third is to make/thrift/mend instead of buying new. While not practical for all things, I certainly have sufficient clothes, but I'm finding myself doing things like patching a ripped seam in my undies (they are perfectly useable otherwise!), darning socks, and knitting up things we might want. I am a crafter, though, so I also have all the materials around, so if I'm making something new, I'm generally trying to use materials I have on hand instead of buying new materials because that would defeat the purpose, so yay for fabric/yarn stashes. And the spouse is taking advantage of some time to browse thrift shops for things we want--and I'm trying to make lists, like telling him to find me yoga blocks at the thrift shop instead of buying new ones, or looking there to replace our waffle iron (which is better for the environment anyway).
Finally, it also helps to have fewer expenses, like being able to get through undergrad/graduate school without loans (or being able to pay off the small loan I took out quickly), not having a car payment, and not having to pay for childcare. This series of circumstances reminds me that where I am is a mix of good fortune, resources, and other things outside my control (along with a few choices we made).
I meant for this to be a little tongue-in-cheek, except as I wrote it, it got earnest. Mostly, I want to point out that the combination of luck, lowered expenses, increased funds from outside my job, and other factors that I had little control over actually helped me out--and I'm leaning into a year of being more deliberate with how I spend money (and using all our skills to make things more cheaply).
And as I told my partner, the goal wasn't austerity but frugality, and I think we're seeing how making a little less money isn't so bad because we have enough overall, which isn't the case for a lot of families. When I was younger, I didn't have enough--my family was poor in the full definition of the word, and I had to get to a point where I had enough in order to break the boom/bust cycle of spending that happens when you never know if you'll get a windfall again (basically, after I got this job). But now that I've had sufficient resources for long enough, I'm able to manage--and have a safety net too. My financial security is still something I marvel at and feel grateful for every day. And I'm glad it can support this sabbatical year that I sorely needed.