Off the top of my head, you could re-do old missions that have ship equipment (shields, deflectors, engines) and sell those. The Breen space equipment, for example, sells for 100k to NPC vendors on space stations (remember that you lose 25% of an items sale value if you dump it into your replicator). However, those missions can be kind of time consuming, and I think you can only re-do them once a day... but that's still 300k a day if you repeat those missions daily.
The Universe Race event, or whatever it's called, is a great way to make money -- I've heard of people equipping Borg engines and zipping around multiple times. You earn 325k (I think?) for each successful run, and with the Borg engines you should be able to easily get around twice, maybe three times if you're good.
(EDIT: Tour the Universe event! Thanks, Thoroon.)
Some people buy up tons of Keys on the C-Store and sell them on the Exchange for tons of EC, but not everybody has a lot of extra money to throw at the game, or would really want to if they did.
I personally make almost all my EC just from selling junk that drops in STFs. It's not exactly rapid cash gain, but if you're lucky and score a bunch of ship equipment, you can make over 100k after a 15 minute space STF.
I'm sure someone will poke in here with other, better ways... but those are the ones I know of.
There are several easy ways for EC (=Energy Credits):
1. Tour the Universe - Hourlong Event, look up Calendar - Starts at Earth Spacedock/First City
Nets you 350.000 EC per Run, you can manage to do it 2-4 times in one hour.
It's merely just flying around, nothing more. See STOwiki: Federation tour example.
2. Buy unreplicateable Material for Dilithium - Memory Alpha:
Either buy the common ones (way more profit, but takes more time to sell) or Uncommons (sell instantly during Crafting Event).
8.000 Dilithium net you around 500.000EC with Uncommons, 1.500.000EC with Commons.
3. Do Fleetactions:
Nice place to get stuff to sell (sometimes worthwhile for Exchange). Flying around, destroying ships, getting to know "nice" people.
4. Buy Items on C-Store:
Some Items are quite valuable, for example Bridge Officers.
Usually Number 2 is more profitable though.
Do Explorations, scan for unidentified objects in any cluster/nebula you prefer.
Sell rare samples on Exchange or use them for crafting.
Selling directly is easier, crafting requires time and knowledge of the market.
Best, most profitable way: Play the Exchange AKA feel the Ferengi in you
Rather dull way to make EC, but very profitable if you know the market.
It's all based on buying stuff and resell it for larger profit. Even small margins help. Timeinvestment is very low longterm. You need some EC and Time to start.
There are no certain ways though, you really need to check and invest some time at first for items which sell quick. If you know the rules, you spend less then 20 minutes per day for very large profits. (Be a Ferengi)
A Hint for start ups: Mystey Lockboxes
Buy cheap (for 10.000 up to 12.000 EC each) during night/day, sell for 18.000 EC and more in the evening.
Do this 40 times (takes less than 5 minutes), easy 250.000 EC and more.
(Note: there is no guarantee it always works this way)
There are many many ways to play the exchange, but a true Ferengi doesn't tell
I'll add that doffing can reward you if you're dedicated to it. The Childrens Toys chain has a couple items of value, the first part grants a Strange Alien Artifact which sells for 650-800k depending on how the market is. The second part of the chain uses the Strange Alien Artifact along with 1 particle trace of each kind to make a Powered Alien Artifact which sells for 1-1.2mil ec. Then the third part which needs good doffs to have a chance at converting the Powered Alien Artifact into a random MK XII console, depending on result it can yield a lot of ec but again the last part has an element of randomness.
If you dont like doffing, you can always recruit doffs from the acadamy assignments and use the convert 5 doffs of a lower quality into 1 of a higher quality (5 white->1 green/5 green ->1 Blue/5 blue->1 Purple), this costs dilithium to do, not a lot but again it's random as to what doff you get but some doffs sell very well.
You can also run elite STFs and sell MK XII loot for decent returns or watch the exchange for trends and pay attention on upcoming events or patch notes to spot something that may become valuable or less valueable, eg whenever a new lockbox is released master keys will increase in cost, buy them cheap sell them high.
Man is a gaming animal. He must always be trying to get the better in something or other.
Warning, this poster tends to talk nonsensically when caffine levels fall below 80%.