In case the buffer system of your RE supplier does not provide a suitable double digest condition you can also resort to sequential digest, purifying the DNA after the first digest with a kit for PCR clean up (use tris buffer without EDTA for elution). When complete (double) digest is required (cloning) this is often the better option.
If you check the DNA fragment by REs, you can use this protocol: 1x (0.5ul of REs, 1.5ul of 10xBuffer, D.W up to 15ul of total volume). If you do cloning, you can use based on manual instruction of REs but my usual protocol is 1x (1.0ul of REs, 2.0ul of 10xBuffer), D.W up to 20ul of total volume). Incubate at 37oC in 1-2 hours.
The conditions depend on the company of the enzymes. In general, in double digestion reaction you need to select a common buffer which gives 100% activity for each BamHI and EcoRI. If not possible, you can select a buffer which gives 100% activity to one of these enzymes and 70-100 % activity to the other enzyme. For example if you ordered these enzyme from Promega, you can use the multicore buffer as a common buffere for the 2 enzymes in the reaction mix because it gives 100% EcoRI activity in the reaction mix and gives 75-100 % activity to BamHI in the reaction. You can not use the buffer comes with each one as a common buffer in the reaction mix. The buffer which comes with EcoRI is called "H" and the one which comes with BamH I is called "E". You cannot use either one in the double digestion reaction mix, because if you used buffer H in the reaction mix, EcoRI will work with optimal activity (100%) and BamHI will not work (0% activity). Vice versa will happen if you used buffer E.
For example, according to the instructions of Promega you can set up the following reaction: