Help with lawn

[Lloki]

Hi, I really don't have a clue when it comes to gardening and need some help.
I have a small lawn, it's uneven, and has dips, in the rain it gets boggy which never used to be an issue until we got a dog. Last winter as it was boggy and muddy, with him walking all over it, it was basically like a mud pit!
Now I've basically got barely any grass left and I'm just left with dry
dirt.
So firstly I need to try and sort the dips and one quite big hole to hopefully stop the water settling in there and then I need to grow the grass back!
I can't spend a fortune on this, please tell me there is a way of at least making it slightly better without spending a fortune?

I also have a miserable, small “lawn.” There is more moss, clover and dandelions than the lush grass I dream of. Next door’s fence casts quite a wide shadow down one side of it and there is builder’s rubble under the turf. After futile attempts over the years to tackle it with overseeding, lawn feed, scarifying, top soil and sand mixes etc to create a level green carpet I have decided to go with no mow May and let the bees have their haven this summer. In late August I’m going to lay a path and start to take up the weeds / turf to create new beds where I will begin to plant shrubs and a small tree. I don’t have a dog but perhaps, as your lawn is small anyway, your dog might enjoy sniffing about amongst shrubs just as much as digging up the grass. Possibly abandoning the idea of a lawn is a solution?

But, if you are keen for a lawn then you can overseed, feed, water and fill the dips with sand and top soil. You really need a strategy to keep your dog off the grass though.

It depends how far you want to go. I’d put field drains in to prevent it being boggy, but that costs money and makes a bit of a mess for a short time.
If finances allow I’d rent a scarifier, fill in the holes and straighten it out, put lawn weed killer down, then reseed.
You need to water it when it’s dry like now.
Do you have a patio ? If you do you might need to restrict dog to that when the lawn is muddy.