What's a good way to start making money in OpenTTD?

In Temperate or Subarctic climates, delivering coal to power plants is an excellent start to your budding trade empire. Coal also has no late delivery payment reduction, so you don't need to worry too much about getting it there in a timely manner. You can find a power plant all the way across the map, and as long as you can afford laying the track out there, delivering the coal there will pay a good amount. If you find another coal mine along the way, you can build a Feeder Bay, drop the coal off there, and let a train from this mine deliver the coal the rest of the way.

If you're not in a Temperate or Subarctic climate, take a look at these industry flowcharts. You want to choose something simple, a single item deliver that has no output, if at all possible, to start with.

Further, Power Plants never shut down, so you don't have to worry about suddenly having commodities available that you can't deliver. The coal may run out, but that's a pretty simple logistical problem; just deliver the rest, and then sell the train(s).

Now, it will take some patience, but what you can do is focus on a single route at a time, and ensure you're getting maximum profit from it. If you have a train on a single track that always takes a full load from the mine, and there's some leftover, add more cars to it until it can pick up ~95% of its capacity the instant it gets there. That will lower the amount of wait time to fill it up completely, and ensure the amount waiting doesn't decay too much.

If you have a super long train already, and you still can't carry most of the coal, then it's time to twin the track. Either two side-by-side, each with its own train, or a each side a one-way, so the trains go in a big circle. Turning it into a big loop also ensures you can place more than two trains on the same track.

Once you've tweaked your first route to be as efficient as possible, you can either go create another one just like it, or you can start building your fledgling trade network.

Once you get a decent amount of cash in the bank, you can start building sections of a multi-part industries, such as Iron Ore --> Steel --> Goods. Start on one section at a time to avoid bankrupting yourself, and start at the beginning. First deliver iron ore to a Steel Mill, and follow the tips above. Once you've got that straightened out, start delivering steel to a Factory. The hardest part of doing this is figuring out how to manage the trains that are delivering and picking up goods.

You can build trains that go along the entire route, but they won't be very efficient. It's better to build dedicated trains for each type of good, and let them handle their own sections. You can see some pretty good examples of how to build advanced stations from the OpenTTD Wiki.

Apart from cheating you mean? Well i still find this a bit of a cheese but it just uses the game mechanics. What i normally do when i just want to continue building is starting a couple of aircraft lines. First take on maximum loan and build 2 or 3 airports at 1500+ cities then buy two or more airplanes and let them fly between those airports. Since they are fast and often carry 100+ passengers they provide a very good income.

You do not want to build your airports to far away since it takes too long for the planes to get service and they will fly a lot slower (when smoking). I usually eyeball the distance on max zoomed out and a full screen distance. But this does not make sense if you play a different resolution on a different monitor/window size so I say not more then 200 tiles apart.

Fast forward and build a couple of more airplanes, repay your loan and your good to go.

Do not forget to replace the airplanes after a couple of decades or they will come down the hard way.

Another way would be to have a two-way track across a couple of cities, let some trains run between those until you are on good standings with the cities. Now those cities will grow pretty fast. And you can add more stations and let some industry products come in. This is definitely a slower way of making money early on then taking the airplane route but it feels better imho. I advice to leave enough room on the two-way rails so you can add another rail when there is a high volume of traffic later on.

Build lots of routes from coal mines to one power station, and when you have enough money, start a separate network somewhere else and expand it from there, also expanding the coal mines to power station route. This is a slow way to make money, but it can be more profitable than aircraft