I think it depends on a few things -

Do you have a reasonable budget - if so, i'd re-turf it - as it's small it would be fairly cheap and much easier.

If you DON'T, dig it over and get the area prepared and then seed it - this will require you keeping neighbouring cats and pidgeons off the seed, obviously, which can be no mean feat !

Late summer to early autumn is the ideal time to sow a new lawn while the soil is still warm and damp and it will cost you less than turfing. There are different grass seed mixes to choose for your garden conditions such as shade or hard wearing etc.
Prepare the soil by skimming off your old grass, removing large stones and weeds, Fork it over and rake level leaving a fine finish. Firm the soil by walking over, placing weight on your heels and rake again. Gently rake in a granular fertiliser about 2 days before the seed is to be sown, cover the area with strings to keep of the birds and sow the seed generously and water.
Turfing is instant but you still need to do the above preparation.

Examine the lawn you currently have - if two thirds of it is weed infested, dig it over and start again. If, though, most of it is fine, but with bald patches, then do repairs. You will need the weather to be fine when you work, but the ground should be damp. Aerate the whole thing first by going over with a fork, pushing it in by standing on it, then pulling it straight out again, to make holes about every 8/9 inches. Rake over hard the bald areas, to make a tilth of fine, crumbly soil at least one inch deep, preferably more - if the bald areas are large, might be easier to achieve this with a small garden fork. Add a little Growmore, rake and level off and apply seed - can be done now provided you're able to keep it well watered, particularly once the seed germinates, but you won't be able to use the lawn normally for some 2 or 3 months. Alternatively, wait and do it in September - germination is usually fast even then, and its got the winter to settle in. Cut with shears or a good hover mower for the first 2 cuts.