Hi,
I moved into a new house the the grass was a bit patchy and yellow in areas so I decided to have a go a reseeding it. Posting here in case it helps anyone else thinking of doing the same / if anyone has any tips. After a lot of online research here is what I did...
Pre Work:
Weeding
I went up and down the full lawn by hand and pulled out any weeds by the roots. It's amazing how many there were when I got down close to the lawn and really looked. I found this tool to be fantastic for getting all the way down to the roots...

Mowing
First I mowed the grass short. I wanted to get the seed as close to the soil as possible and didn't want it sitting on top of taller grass. I'm not sure if that's correct, I made this bit up my self! Here's how the grass looked then...

Aeration
As my soil is very compact and clay like (would be great for tennis but not growing plants!), i tried to aerate it. I got a manual aerator in B&Q for a tenner.

This didn't really work for me, the spikes got clogged up every time, so I was making holes, but more so by pushing the soil down into the ground, and possibly increasing the compacting ;(
I did about 1/3 of the garden like that, then I switched and used a garden fork for the rest.
Thatch
Next I used a steel rake to remove the layer of dead grass / thatch that I could see below the green grass. I was surprised how much the rake pulled up as it didn't look like there was so much there. There is a better / proper rake for this, but I just used the one I had.

That's all the pre-work, the garden is ready for the seed now....