Yes, recommend practising on the old sheet, just cut, pin and sew at random to get used to joining fabric, cutting, etc. There's nothing you can do wrong with that. Other than that, you can get plenty of old sheets from charity shops (esp childrens') that will make over well into toy bags/PE kit bags, etc.
I bought a 1970's retro flowery sheet off eBay that we're going to make into aprons (take home presents) for my DDs friends at her cupcake decorating party. (I know, very Kirstie Allsopp and slightly nauseating, but she's really excited!!) And in the long-term, about the same cost as a whole load of plastic tat from the pound shop.
As you get more confident, you can cut patterns off things you already have - just lie it flat on top of your new fabric, and cut around, leaving about an inch all the way round for your hem. (I'm thinking aprons here.) There are tons of things online about it, suggest watching a video first.
I've had a sewing machine for about 20 years, on and off, and I learnt after awhile that the only thing you CAN'T undo with making your own things is cutting. You can always unpick sewing that's gone wrong. And ironing/pinning things first shows you if it's going OK. Just measure twice!!! It's only ever cutting that makes me nervous.
And I do very little dressmaking, it's difficult to do it well (buttonholes/collars/cuffs, etc.) And I'm too impatient!!