Ground is the common negative - the frame. Eventually, everything is connected to the frame and through this to the battery negative.
With the tester you have the available tests are somewhat limited, you can test for a ground (sort of) at the relay socket though... For normal use, you have it connected correctly with the clip/negative lead to the battery negative terminal.
Put something like a paperclip (or other handy sized bit of metal) into the hole for 85. Connect the tester alligator clip (-ve, negative, black lead??) to this and the other side of the tester probe (+ve, positive, 12v, red connection??) to the battery positive. When you press the starter this should light up briefly. This test won't tell you how good the ground is, like a proper meter would, but it's a rough indication.
You could see if the relay is operating (at least mechanically) if you have a couple of spare bits of wire - connect pin 85 to battery negative and pin 86 to battery positive - the relay should click...
Also, maybe try another relay? Any 12volt relay with the same pins in the same place will work - there is nothing special about the BMW relay. 15Amp should be sufficient, 30Amp is probably a better long term thing.
Alternatively, find someone with a proper multimeter who knows how to use it and get them to follow the tests Inge described - they are 'better' tests that will tell you more.