There are many species of Buttercup. You are most likely to find Ranunculus bulbosus (Bulbous Buttercup), R. acris (Meadow Buttercup) and R. repens (Creeping Buttercup). You can tell these three apart by looking at features of the flowers and leaves.
1. Look at their flowers. They all have 5 yellow petals. Below these petals, there are 5 greenish yellow sepals. In R. bulbosus the sepals are folded down (‘strongly reflexed’), while in R. acris and R. repens they are lightly pressed against the petals (‘erect’). Also, the flower stalks are furrowed in R. bulbosus and R. repens, and are not furrowed in R. acris.
So if the sepals are reflexed, you have found Ranunculus bulbosus. If the sepals are erect, go to step 2.
2. If the sepals are erect, then look at the leaves from near the bottom of the plant to tell the difference between R. repens and R. acris. These leaves are made of several leaflets. In R. repens the end leaflet has a stalk, while in R. acris it does not have a stalk.
So, if the sepals are erect and the end leaflet has a stalk, you have found R. repens, if the sepals are erect and the end leaflet does not have as stalk, you’ve found R. acris. R. repens leaves often have white patches on them too, and unlike R. acris it creeps by runners.