When you get it home, take the balls out, take the playfield glass off, and put the table up at ninety degrees. Most machines have a bar in the bottom right of the cabinet to use as a "prop bar" - and there should be a metal bracket that the bar can go into. Look around at all your PCB boards - look for any burned areas on the PCBs - look for any fuses that could be missing or blown. Do a visual once-over of the underside of the playfield, looking for any missing bulbs, loose wire from broken solder joints, or any loose screws/bolts at the bottom of your cabinet. You don't have to do a complete and thorough inspection - just look for things that look "out of place". Once you're satisfied, put your playfield back down and proceed to the translite...
Unlock and remove your translite glass - make sure all the bulbs are back there behind the translite (you'd be amazed how many could be missing. Your translite backdoor where the bulbs are mounted is hinged like a door with a latch that you will pull straight up on, that releases the latch holding that "lighted swing door" stationary, and you should now be able to move the "lighted swing door" to view the MAIN PCB boards. Look for any burns on the PCB boards/around the black IC chips, or hackjobs such as cut wires or ribbon cables where the ends are not firmly seated in the plastic prongs - typically on the edges of the PCB boards. Check your batteries on your main cpu board, make sure they show no signs leaking battery acid, and I would flat-out just change them for my personal peace of mind.
Once all that's been done, re-seat your translite backbox door and don't put the translite glass back on. Fire up your new machine by flipping the toggle switch - it should typically be on the underside of the cabinet near the bottom right leg. After 1-2 seconds at the most, your machine should come to life. Look at your translite backbox door - are all the lights on/flashing ? Look over your playfield, visually see that the majority of your lights are active. Some obviously won't be; the behavior of your lights varies from one machine to the next depending on the manufacturer and the title of the game. Get your manual (if you don't get one with the game, go to ipdb.org and download the one for your game), and read up on how to do all the tests - most notably your lamp test, light column test, coil test, and flasher test. Everything you desire to test is strictly up to you - those are the first things I check.
Once all that is done, TURN your machine off. Reassemble your translite and lock it in place. HANG YOUR TRANSLITE KEYS on the inside of your coin door - nearly every machine has some kind of clip inside the coindoor that the keys should hang in. Put your playfield glass back in place and re-seat your lock-down bar. Lock your coin door (make sure your game is on free play ), turn your game on and enjoy! Look for anything not behaving as you play and take mental notes.
Come here, tell us what problems are, get help, fix problems, play game, note that you need another pin, buy another, get it shipped, wash, rinse, dry, repeat .....
Oh, and to help you out, here at Pinside, Starship Troopers = SST