Here are two really good, really easy ways to make ramen with eggs:
The easiest way is to just boil an egg and toss it in. If you eat this a lot, you can boil a few and keep them in the fridge. They should stay good for about 3-5 days. If you like liquid yolk in your soup, soft boil the eggs (boiled between about 3 and 9 minutes, to taste). Just cook your ramen, peel the egg, and drop it in for about 90 seconds right before you eat it. Cut the egg in half if you like. It is best to use older eggs for this. What I like to do personally (and remember this comes from the internet, so listen to me at your own risk) is use them for boiling if they have passed the expiration date, since that date (in the US) is based on the thickness of the egg white, not food safety. Older eggs don't stick to the shell when they are boiled, but new eggs do.
The slightly harder (but tastier) way is to poach the egg in the ramen. To do that, cook your ramen, and make sure you have tasted your broth and you like it. If you don't like the seasoning pack from the ramen, you can add any combination of soy sauce, grated ginger, crushed garlic, oyster sauce, miso paste, sriracha, etc. There are lots of tasty, cheap things to add depending on where you live. Try them! Anyway, back to the eggs... You want to cook the ramen until is is soft but not cooked all the way. Turn the heat down to almost nothing. Crack a very fresh egg (fresh eggs have a nice thick white) into the pan once it stops bubbling. Give it a few minutes. If you want to feel busy, you can spoon the hot broth onto the top of the egg to cook it faster. If you are particular about how cooked it is, jab a knife into the middle of the yolk and check it out.
Here is the last egg and ramen tip: My friends and I just called this noodle slop, but it tastes good, uses fresh at least a few fresh ingredients, and is super cheap. Cook some ramen noodles and drain them. In a big skillet, add some oil and fry some combination of celery, onions, chopped cabbage, ginger, fresh chili peppers, garlic, matchstick carrots, bell peppers, chopped scallions, cucumber, zucchini, etc. You want to cut them to the size you get in Chinese takeout and cook them until they get a bit soft. Then, scramble one egg per ramen package in with the veggies. When the egg is cooked, add the noodles and mix it all together. Add some salt and pepper, or the seasoning from the ramen if you are into the whole MSG thing. It is like cheap chow mein.
The basis for any sort of Japanese soup dish is going to be dashi stock, a stock made of fish and seaweed. It has a much lighter flavor than chicken broth, so you might not have identified it easily. You can buy it in a powder form for convenience, and it can be sprinkled into other liquids rather than reconstituted.
This recipe is for soba with a dipping sauce, but it'll give you a good idea of the flavor profile you're looking for: Dashi stock plus kaeshi, which is made of soy sauce, mirin, and sugar (and simmered so it's not strongly alcoholic).
Best Answer
I don't recall ever seeing regular onions in my ramen in southern Japan (but scallions, maybe--it was many years ago, so it's hard to remember). As for topping oil, the only one I ever saw was "Chinese fire oil", which was usually provided on the side for addition at the customer's discretion. I loved the heat from the fire oil but could only stand at most a few drops. It's the hottest stuff I've ever tasted. I brought home the bottle I had, and I still have it (though the wife and kids don't like anything anywhere near that hot, so I haven't used it in years and it's very likely rancid now). In the two years I lived there I only managed to use a few ml. I can't imagine that the 5 oz. bottles at the grocery store and on Amazon are the same stuff. Here it is: