This recipe works very well with strawberries, and also with fruit that doesn't agree with cream, like various kinds of melon. It has to have some substance-- juice only, like citrus, won't freeze to the right texture. Still working on that.
Put the fruit through a sieve or a puree sieve or liquidise it in a blender. Add lemon juice or other flavouring as needed, then mix in sugar syrup until it's considerably sweeter than you want the frozen stuff. When the unfrozen mixture is as sweet as commercial sherbet it's probably exactly right.
If you're adventurous, try making strawberry sherbet with somewhat less sugar, balsamic vinegar instead of lemon, and some pink pepper.
Chill the mixture for about half an hour, then stir, before putting it in the ice-cream maker.
If you don't have an ice-cream maker, fill a metal box (such as a cake tin) with the mixture, cover with foil and put it in the freezer. Alternatively, use a box you buy ice cream in. Take care not to fill it more than half full, because ice expands! Give it a good stir after one hour, scraping any already frozen stuff from the sides and bottom and mixing it in. Repeat at half-hour intervals until there's no liquid mixture left.
It's best when eaten immediately, but you can keep it frozen in a tightly covered box for a few weeks. Put the ice in the fridge half an hour before you want it (or before dinner) so it can get soft enough to scoop.