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Trackers are one way. Another way is to take a series of short exposures, hand-tracking the stars between stars with a tripod or home-made "barn door" tracker (look it up), fix the alignment to pixel precision in post, and add the images all up, utilising appropriate denoising algorithms in the process. It's tedious with 300mm though, you'll need to stack hundreds of shorter exposures to make it work, but it becomes significantly easier (but still not "easy") with 180mm or so. Start with a wider angle lens such as fast 35mm or 50mm prime for your first astophotography shots and work your way up from there as you succeed in building your technique. If you want to go with stacking rather than a motorized tracker, try stacking 3-4 images using a 50mm first and establish a post-processing workflow before you try to stack 100 images with a 300mm. If you are fluent with signal processing you can write code in MATLAB, Octave, or similar tools to make the alignment process automatic.
Second, check that your focus is accurate. I highly suggest using manual focus in 5X LiveView with a relatively bright star to set your focus. Autofocus is unlikely to work well, and with your 300/2.8 even a slight bit off infinity and you'll get essentially nothing in the picture. This is where manual focus lenses with hard infinity stops are useful because you can confirm their calibration in the daytime with some faraway buildings, and then just slap the lens to infinity (or wherever you measured infinity to be) and shoot at night (barring temperature changes to focus which you should be aware of if it's significantly colder at night where you are). As a bonus, good manual focus lenses suitable for astrophotography come cheap.
Third, make sure you're in a good place with as dead zero light pollution as you can get. Camping in the middle of national parks and deserts is usually a good place to be. If you live near an ocean you can also try going to a beach and shooting into the ocean where light pollution will be minimal. The Andromeda galaxy is visible to the naked eye (it looks like a bit of an oblong, fuzzy star), so if you're not seeing it with your eye, your camera isn't going to see it either. It's also not very easy to shoot good pictures of Andromeda when even the moon is out.
Also, make sure you're shooting RAW. Always. In-camera noise reduction doesn't work well for stars, and you'll want the full dynamic range to work with in post-processing whether you're doing stacking or not. If you stack images, make sure your workflow supports 16 bits or (better) floating-point images and do not use any lossy compression formats until you have your final piece.
Finally, astrophotography is also highly affected by atmospheric conditions and turbulence. You'll have to try many times on different days. It takes a lot of patience but is rewarding. Good luck with your new hobby!