Firstly if it’s freshly laid turf, just keep the water up to it until the weather starts to warm up a bit.
I’ve laid about 800-900m2 of Buffalo at our place over the last few years.
How much care it needs depends on the time of year, but we’ve done a few sections in late winter and I prefer to hand water for 30 minutes every 2 or 3 days for the first few weeks. Just to make sure it gets a good even soaking and stays healthy until there’s a few more hours of sunshine in the days.
1. Mowing - cut it reasonably long for now. Next summer (as in Nov-Dec next year) you can go a bit shorter when it’s growing fast, but for now keep it longer.
2. Fertilizer - I don’t get caught up in brand name stuff for many things in life, fertilizers are no different. My pick is palletized chook Shit. Wait till Oct-Nov before you feed it, you might get away with feeding a bit earlier in Sydney, but north of the boarder it’s just a waist to start feeding until well into the storm season and the rains are a bit more consistent.
There’s a hole bunch of crap written on fertilizer bags these days, but as long as there’s actual crap inside the bag, that’s all that matters.
3. Increasing coverage- wait for winter to end and in the mean time make sure you’re hand watering in all those gaps so the edges don’t dry out.
4. Watering- See above.
In summary;
Look after it for the first few months. Feed it once a year when it’s raining.
Cut it reasonably long and as often as you want to see your nice green lawn looking great after it’s been freshly cut.
Edit: Tryagain just beat me to it....