Well, the first thing I do in the autumn, when the blackberries are ripe, is to make a gallon of blackberry wine. Of course this isn't quite so convenient if you don't have the right kit but it's possible to do with a clean gallon bucket (sterilise with boiling water or 'miltons' type stuff).

Put the fruit in the bucket along with a couple of litres of red grape juice (cheap supermarket juice should be ok). Sprinkle in some breadmaking yeast. Cover the bucket with a clean kitchen towel - possibly tie the towel around the top of the bucket so flies can't get in. Cover that with a lid or plate.

After a week or so, strain the mixture into a demijohn or a 2nd clean bucket. Leave it to ferment to dryness. It may be a good idea to get some 'stabiliser' (potassium sorbate) and sodium or potassium metabisulphite (both from any homebrew supplier or somewhere like Wilkinsons).

Add 1 tsp of sorbate and 1/4 tsp of metabisulphite. Give it a vigorous stir to de-gas the wine. Leave to settle before bottling (in sterilised bottles of course).

Of course it depends on how much fruit you have but it's possible to make a pretty good wine following the above procedure.

Alternatively, make a blackberry crumble.  That's my second favourite use for them