I like top lane. I watch streams to help learn and I sometimes see the same person building dorans on say... Olaf instead of a phage or warmogs. When do you go for dorans over bigger items?
This strongly depends on the match-up and how well you're doing. If you're against someone who you can trade against easily and always come out on top in said trades getting a Dorans will generally be a better idea because it'll improve your damage more than low level alternatives. This is generally true if you're playing a champion that hits harder versus a more tanky champion that doesn't deal as much damage. Say Riven versus Cho'gath for an example, Riven would probably want to grab x2 Dorans before going into her build to give her more damage potential on Cho'gath since she normally comes out on the good side of trades.
Alternatively, if you're getting bullied pretty badly you can always go for Dorans items (they're fairly gold efficient), though I'd probably recommend getting a Wriggles because of higher sustain and the damage reduction. A lot of top lane is knowing your preferred champion's match-ups and how well he/she trades against their enemy in lane.
For a little bit a math on Dorans Vs Wriggles I'm gonna add a link to another answer on here. Just for Context: The question is about Dorans Vs Wriggles on an AD carry, but the math still applies universally. https://gaming.stackexchange.com/a/59537/7494
Additionally, if you get fed early and can afford beefier items you should almost always go for those, but getting Tier 2 Boots, x2 Dorans, and a cheap defense item at low levels will almost always be better than trying to save for a 1.5k+ gold item early.
Hope this helps :)
Simply put, Doran's items give the most bang for their buck. Their biggest disadvantage is that they cannot be built into better items and thus tie up an item slot, but that only becomes a problem 25 or more minutes into the game. All Doran's items are focused on sustain (lifesteal and regen), and getting early sustain is very important for getting gold and xp.
However, watching high level games can be misleading. High level players are very skilled at avoiding damage and getting their farm and xp, and they don't make a lot of mistakes. Also, they usually play draft pick games (Normal or Ranked) so they know who they are fighting against before buying their items and can choose appropriately. At your level you will likely make lots of mistakes and be punished for them, and if you play Normal Blind Pick you may not know your matchup. In both cases Doran's won't save you; you need other starts like boots and 3 pots for escaping and healing, or armor and 5 pots for super hp regen.
For example, I play Olaf top with armor and 5 pots. Given the current meta I know I will be matched against an AD solo, so the armor will reduce damage they deal with a Doran's Blade. Also, I can use my 5 pots to heal a total of 750 hp, allowing me to ruthlessly Reckless Swing them. If they show up with a Doran's Blade or Shield, not only do they not reduce the damage from my Reckless Swings (True Damage), they have no way to quickly heal from the damage so they cannot contest me in lane. I will pound on them until they have to go back to base, giving me an advantage, or they will mope about in lane while I keep them from their creeps. Playing at my level this is a 90% success strategy. Playing Ranked against pros they will pick a champion who can lane against Olaf (say Riven, Cho' Gath, or Vladimir) and will probably beat me in lane.
Nonetheless, figure out if Doran's works for you. Watching streams will teach very little about playing at your level - the best way to learn is to try it!
Usually if you get ahead in gold, buying a doran's blade will instantly make you stronger in that moment with that extra gold. Which will help you in your lane at that exact moment. Unlike items that cost the same as a doran's blade which will only be better when you make them into a complete late game item.
Doran's Blades offer every stat most bruisers deem valuable in the early laning phase: Health, Life Steal, and Attack Damage. The major drawback is these items do not build into anything late game, and your opponents will quickly out scale the early advantages this item offers. You should buy Doran's Blades Top Lane when you feel they will give you the necessary advantage to win the lane. Buy GP10 Items such as Heart of Gold or Philosopher's Stone to Catch up in lane you're losing instead of Doran's Blades.