We have only a small flock of sheep - mostly self-shedding Wiltshire Horn sheep, but we also have a growing collection of coloured Merino and Crossbred sheep. The Wiltshire Horn ewes are a hardy bunch and normally birth with few complications and are good mothers.
Sometimes however the weaker of twins is rejected and if we find it in time we end up with a poddy. Or a local farmer with a soft heart wants to keep an orphaned lamb alive but hasn't the time to raise it.
Larger scale sheep farms often have a set-up with a designated pen and buckets with multiple teats to raise a commercially worthwhile number of lambs. We start off with a large cardboard box in front of the fire. As long as you put some bedding in it and don't keep the lamb in there so long the urine soaks the bottom out, it works well.
We try to keep some calf colostrum in the freezer for such emergencies (cross species colostrum is way better than no colostrum). If you haven't any, try a local dairy.
In spring our local supermarket stocks plastic teats suitable for lambs. If desperate a baby's teat will do but lambs need a much longer teat to be able to suck it comfortably without assistance.