By group I mean they can be rotated, translated and scaled together, but still can be edited separately, and use their own modifiers.
You can select all the objects and hit CTRL+G, to create a group. Another way is parenting objects to each other with CTRL+P.
Keep in mind that in Blender, groups are more of a suggestion than a direct order.
For example, if you select one object in a group and move it - the others do not follow. For that you either need to do something more forcible (like parenting, as LuisEDB mentioned), or you first do Shift+g,g to select the group before you move.
Another interesting behavior is that duplicate objects inherit the group from the original object. This means that if you have a group of objects selected and you Shift+d them, to make the new ones a separate group you will have to Ctrl+Alt+g and hit Ctrl+g again.
Not sure if you wanted this info or not, throwing it out there anyway.