Stardew Valley

You don't have to fish at all, even for the community goals. You can also buy them from the bazaar cart or get them out of the trash and they don't even have to be in season. But these are also subject to RNG and even less fun.

If you're still willing to try Stardew Valley (I understand there's a 1.7 update coming out sometime):

Honestly, the thing that helps me absolutely the most when fishing is changing your zoom level. this works on the PC, I'm not sure how well it works on other platforms: Whenever you get to your fishing spot, zoom your screen in like ... I dunno, maybe 5-6 times? When you cast your rod, the fishing bar will be a lot larger. I find it almost impossible to catch fish with a zoomed-out bar, because the movements you need to make on the mouse become so fine relative to the image presented. By zooming in, the fishing bar is larger and your movements don't need to be nearly so fine. I honestly can NOT catch fish if it's zoomed out too far. [If you're too far zoomed, the ends of the fishing bar will disappear off-screen; just quit fishing and re-zoom to someplace you're comfortable with.]

Other stuff:

Go to Willy's and buy some fish stew; that'll get you a +1 on your fishing skill.

If you have the Sewers or Secret Woods open, go there; otherwise the Mountain Lake. You're fishing for Carp; they're pretty much the easiest and most common thing to catch, as they don't move around much and move comparatively slowly.

In the Sewers, the only fishable items are: Mutant Carp and Radioactive Carp, both of which you can stop chasing immediately; Green Algae, White Algae, and Trash, all of which pull up immediately (and catching trash still counts toward your fishing skill); and Carp. In the Secret Woods, the only fishable items are: Catfish, which only occur during and will bounce around quickly and you can ignore; Woodskip, which will bounce around a bit; and Carp. [Can't remember if the Secret Woods has trash or not.] The Mountain Lake is your last resort, as there are a number of different other fish that can be caught there, though you can maximize your chances of getting Carp by casting as close as possible to the shore.

Eat your fish stew. Cast your fishing line as close to the shore as possible; this will minimize the number of other fish you'll catch, increasing your likelihood of getting Carp [and trash, but even catching trash counts toward Fishing skill level]. When the line twitches, don't pull on your rod - like I said, Carp don't move very fast. When you do need to move it, don't down the mouse button to move the fishing area, that'll likely move it too far/fast for Carp (though it's a good idea for other fish). Instead, gently and repeatedly tap your mouse button to keep the fishing area behind the Carp. Ideally, later on, you'll want to try to keep the Carp in the upper portion of the fishing area, as the fishing area moves down slower than it moves up so you need more "down" response time, but in the beginning just having the area anywhere behind the Carp will do.

Aside from actively fishing, don't overlook foraging for crab pots. Almost all of the items you need for the Crab Pot bundle in the Community Center can be foraged from the Beach; the one exception is Crab itself, which you can get from the Mines and the Travelling Cart. The reward for the Crab Pot bundle is three Crab Pots. Which, I know, you can't use because you don't get access to bait at Willy's until you reach level 3 fishing. However, you can befriend Linus and get his 4-heart event, which gets you access to Wild Bait, and you can use Wild Bait to bait the Crab Pots. Everything you harvest from a Crab Pot goes toward your Fishing skiill, including trash. Once you get level 2 fishing, you can purchase regular bait from Willy.

As your skills advance, you can buy a higher level rod that allows bait to increase how fast fish bite; and later you can buy another higher level rod that allows you to attach different types of tackle, with different effects. The Cork bobber expands the size of your fishing area, and it's one of my favorites.

Don't forget to check with Gus on what the special of the day is; sometimes he sells a special that has higher fishing buffs, which can be useful. You can check what the special is simply by calling him on the phone when you wake up; his answering machine will pick up and tell you what the special of the day is.

If you use MouseyPounds' Stardew Predictor, it'll tell you what the Travelling Cart has for sale each day (so you can tell whether you need to save up money ahead of time, or run over there to buy something particular); and it'll also try to predict (these predictions are less accurate) what items might be found in various garbage cans, in case any of those are helpful as well - trash cans occasionally have fish in them. Trashed fish don't count toward your Fishing skill level, but you can use them in Community Center bundles or cook with them.

And these are all really cool tips and hints, but honestly, again, the one thing that helped me the most with fishing was to change the zoom level on my screen.

Sincerely, someone else who hates fishing in the Valley

I want to play again, but I think I'm going to wait for 1.7 first. And if you haven't modded with Stardew Valley Extended, you really should give that a try as well.