Rotovate, remove rocks/ stones bigger than 3 inch where you can, need to get to a depth of about 6inches. Next, when you wet the soil is it clay like or does it drain well? If it doesn't drain well (also even if it does!) I'd seriously consider like 2 ton of sharp sand, rotovate that in to the soil. Rake roughly level, then walk it flat. Stick another inch or so sharp sand neat on top, rake flat. When happy walk flat. You are now ready to start laying the turf. When laying it, make sure when rolled it's always kept damp, dry roots at anytime means dead grass, I'd consider keeping covered with a wet old blanket /towel especially if sunny. Use a scaffold board /plank to walk on when laying the turves, always slightly overlap each row so you have to almost tuck each row together, if it's hot, they'll shrink and you'll end up with gaps!
Ok, now the important bit, once you are happy, water that lawn.. and I mean water it, good soaking, not high pressure in one area, but nice gentle spray all over, don't miss any, once in morning before full sun, and in the evening. Keep all pests (dogs, kids, missus) off the lawn for at least 4 weeks, ideally 6. (judging by the plot at least 15-20mins per watering session)
First cut, never chop more than half. You want the highest mower setting, and nice sharp blades! Leave a week or so, keep watering although once the lawn is established, cut back to just in evenings. Cut it a little shorter each cut, basically take it a spacer or a notch down each time, each week. You then should have a great lawn, it'll respond great to fertiliser like feed and weed etc, but the hard work has been done in the prep. If the kids/dog trash it, simply returf and it'll be a dream.
Many people neglect their lawn, which is dull really, it's normally the biggest plant in the whole garden, and looked after can make a garden truly special. Personally bare feet on a lawn in summer can't be beaten on a hot day.
When selecting your turf, be realistic, we'd all love superfine bowling green soft grass, but back in the real world if you have kids this will last about 5 seconds.. I have 2 daughters under 10, they love the lawn, realistically I chose a high fescue/rye mix of grass, this means it's courser ie less blades per sq inch but is much tougher, it can take repeated abuse. You may want something tougher still if you intend playing football or have a dog. Subject of fido, if he has to take a leak, a great idea is to keep a watering can full of water handy. Everytime he/she wees, go and water it down with a good half can, it'll stop dead patches and also save shrubs from die back where the leg has been lifted!
Because you have made your soil superfast draining, this will make the grass grow deep roots to find where the water is. Grass will grow roots 6-8 inch in length, at this depth, even in a hot summer, your grass won't go yellow and die off, it will remain alive, even if it's a heatwave and you are on holiday for 2 or 3 weeks! Your grass will be tapping into a giant reservoir beyond the reach of the sun and drought, the grass will grow like this to seek the water, meanwhile your neighbours will be out with the hose/sprinkler every night and still have dead spots!
Sorry to rant on, but hope you understand it's all in the prep work, do it once, do it well, save on loads of problems down the line.. oh did I also tell you about fast draining soil also stops moss? Bonus!!! Hope you find the info helpful and good luck, very impressed with your efforts so far, keep it up!
