There's a couple of ways to go about it, some more expensive than others, some more convenient, and some more flexible. In no particular order:
1) Mic your cab. This is the most inexpensive way, but also the most "limited" compared to the other two. The only drawback I can see would be if you can't turn the amp up loud enough to where it sounds like you want it to. Otherwise, great alternative, it's been used forever and I think we all agree it works.
2) Use an emulated line out device (Mesa's CabClone for example), a loadbox with a line out (not emulated, like the Suhr loadbox), or simply the Direct output on the back of your amp. This way you don't have to mic the cab. You have the choice of using the sounds your emulated line out provides (if you use one of those), or using external Impulse Responses that "recreate" the sound of a specific cab. Keep in mind that if you use the Direct out from your amp you'll have to find IRs that emulate both a speaker cabinet and some sort of power amp emulation.
3) Use something like the Two Notes Torpedo Live which is both a loadbox and a power amp/speaker emulator all in one box (the important part here is that you can choose whether you want just the power amp emulation, just the cab emulation or both). The main difference between using IRs and the Torpedo Live is that, when using IRs (unless you are able to make your own, which I'm assuming is not your case), you are "stuck" with the IRs you can get/download/buy (which is not necessarily a bad thing, as there are tons of IRs out there). However, the Torpedo Live not only emulates the speaker cab, but it also emulates different mics, and you can change the position of the mic respective to the cab in real time like you would in real life.
Hope that helps, cheers!