If you're like me then you are looking for the shortest path to level 10 Antiquities. If you're looking for amazing rings like the Oakensoul or maybe just some decor for your home then I have a few tips that helped me along the way.
In Western Skyrim in Solitude is the guild you need to visit. It has a short tutorial that you should pay attention to. It will go over Scrying and Excavation which are the two steps of this skill. Once you're done with the skill head on over to Artaem.
Open your journal and go to Antiquities. You'll select the green option "Faded Psijic Folio". Then you'll start scrying. You need to connect from the bottom middle to the open slots just like in the tutorial. I really recommend putting skill points into this skill. It makes your life so much easier. Once that's completed open up your world map. It will show you where to head for digging. It's important to note that if you did not connect all the open spaces you will have multiple possible dig spots. Travel around until you get to the right dig site. You will repeat this over and over until level 3. At level 3 you will then put points into Antiquitian Insight. Every green you find will give you a lead to the blue. Once you find the blue then you start back at green. Do this until level 5 and put another point into Antiquarian. Then you can find a purple lead from the blue ones. You can do this once per zone so now it's time to travel the world. At level 7 you can do the yellow leads which can get you the Oakensoul ring.
The biggest piece of advice is that you can bind the Antiquarian's Eye to your quick slots. Using this while inside the dig site will point you to the actual dig site. It's incredibly useful and I never figured this out until level 7. Don't be like me.