This can be done in one of two ways. The simplest is to combine copper and tin ingots together in the standard crafting table (or inventory crafting grid). Before Public Beta 25 this produced two bronze ingots, however, as of Public Beta 25 crafting tin and copper together only produces one bronze ingot, for every pair of copper and tin.
A slightly better way is by alloying the ingots - or their ore variants - together in any kind of forge. If smelting the two ores together, this saves fuel that would otherwise have been used in smelting the individual ingots. It also, unlike crafting tin and copper together, produces two bronze ingots instead of one and gives you the achievement 'double bronze'.
As of Public Beta 25 copper ingots can be used in place of a redstone in the creation of clocks and compasses.
As with other ingots, copper can be crafted into a mineral block for compact storage or decorative purposes.