In order to marry Celia, you need to get her up to 4 red hearts and then propose to her using the blue feather. To make things simple, I've created a system called 'points' to tell how many red hearts Celia will have. 1 red heart = 3 points 2 red hearts = 8 points 3 red hearts = 13 points 4 red hearts = 18 points
There are 2 main ways to increase your points: Give her a flower (or other item she likes) or activate ( and correctly answer) a heart event, which gives you 1 point each. Failing a heart event, may also lead to losing points, but I haven't figured out how many as of yet or if it does.
There are 4 heart events which you can activate during the run (I'll explain the 4th in a separate guide, just pretend there's 3), which means you have to give Celia 15 flowers (or up to 3 more, if you can't get heart events), one every day. Pick up the 14-18 flowers on the first day. There should be 10 Toy Flowers below Celia's farm, and 4-8 Goddess Drops next to her farm. If you're confident that you're going to get the 3rd event, you can miss picking up 1 flower at the beginning and instead pick it up from the spring.
Heart Event Guide:
As mentioned above, there are 3 'normal' heart events which you can get in a run. As stated earlier, there is a 4th cutscene, but it's very complicated, and isn't worth worrying about for a beginner.
The first event happens on Spring 3, from around 1:00pm to 2:30pm. All you need to do, is have 1 red heart, and enter her house, when she's home alone. This will most likely require you to enter her house, give her a flower, leave, and then enter again.
The second event can happen on Spring 5 or 6 (maybe even 7?) at around 10:00am-ish. Basically just leave her house, when Celia is outside, working on the farm.
The third event happens on Spring 8 when you leave your house. I'm not sure it matters whether it's morning or afternoon, but just leave your house to activate it.
If you fail to get the 2nd event, there is a back-up. After the 3rd event has happened you should be able to go straight to her house, enter it then leave to activate the 2nd event. I don't know the exact timings, but it's faster than doing an extra day, but not faster than getting it normally.
However, even if you activate the event, you are given options during the event, which you have to answer correctly to get a point. The 1st event has 3 branching option boxes, the fastest method, is to pick the 1st option and then the 2nd one. The 2nd event has 1 option box, and the correct answer is the 2nd option. The 3rd event has 2 option boxes, both of which the correct answer is the 1st option, meaning you can just mash A during this event. If you're new to the game, don't worry about not getting the 4th event but if you do get it, then make sure for the 1st option box, you select the 2nd option, and then the 1st option for the 2nd and 3rd, meaning after the 1st box, you can just mash through the event.
This covers all the basics of the run. For a guide that lists all/most big and small time saves for this category, that I can think of, read this ---> http://pastebin.com/VCkTzMfk