Like the other cases, there are prepositions which can place whatever comes after them in the instrumental case. There are six in total: С(о), над, под, за, перед, and между.
C(o) + inst means 'with'. This may be confusing, as the primary meaning of the instrumental case on its own is also 'with'. There are two concepts that are both conveyed by the English word 'with', but are conveyed separately in Russian.
'by means of' ('He built it with his hands') is conveyed by the instrumental case on its own ('his hands' in their inst. form).
'accompanied with' ('He built it with her') is conveyed by c(o) followed by the instrumental case ('with her' is c + inst.).
the manner in which something is done ('He built it with ease'). In both of these uses, c(o) inst is the antonym of без + gen ('without').
Над means 'over' or 'above', and под means 'under' or 'beneath'. Под + inst means 'under' if there is no motion involved - if there's motion, use под + acc instead ('The book is under the bed' - no movement, 'The book slid under the bed' - movement). Под + inst can also mean 'physically near', and под + acc can mean 'temporally near' or 'near in time' ('They live near the city' - physically near).
Перед means 'before' or 'in front of' in terms of positioning, and can also indicate responsibility ('The dog is in front of the house', 'The dog walked in front of the house', 'the family has a responsibility to the dog').
Между means 'between' or 'among', similar to среди + gen, 'among' (e.g., 'He stood between them').
За generally means 'behind' or 'beyond', but has a few nuances to it. Like под, when no motion is involved, the instrumental case is used. When motion is involved, however, the accusative case is used ('It's behind the house' - под + inst, 'It went behind the house' - под + acc).