Tips for not going bankrupt
In order to make money, you obviously need to bring in more money than you spend. Controlling costs in the beginning and being frugal can be crucial. Starting small is a good way to achieve this.
Tip: Watch Those Monthly Maintenance Fees
When you buy new ways (tracks/roads/etc), you not only pay a purchase/build price per tile, but you also pay a monthly maintenance cost per tile. Usually the slower track is not only cheaper to buy, but also cheaper to maintain each month. When selecting track/roads/etc, look at the maintenance cost, which is the number in parenthesis. This is also true for stations and station add-ons.
Example: 80km/h vs 400km/h track
The initial cost of the 400km/h track is 30 times the cost of the 80km/h track. The monthly cost of the 400km/h track is 21 times more than the monthly cost of the 80km/h track. The monthly cost of the 400km/h track is more than the initial cost of the 80km/h track!
So for 10 tiles of track, the 80km/h track will cost 400.00 to build and then 20.00 a month. For 10 tiles of the 400km/h track, the build cost would be 12,000.00 and 420.00 per month to maintain.
Elevated Tracks, Tunnels, and Bridges
Elevated tracks, tunnels, and bridges also cost more to build and more to maintain per month. See the above differences in costs for the 80km/h elevated track, tunnel, and bridge compared to the regular track costs from the previous example. Similarly, electrified tracks also add to your monthly costs as well.
Tip: Start off with a small & slow network
Start off by building a small but profitable network. Starting with a simple freight network using inexpensive tracks/roads can be a good way to turn an initial profit. For example, transporting coal to a coal power plant, or oil to an oil power plant. The key is to use inexpensive tracks/roads, which unfortunately will be slower, but cost less. For trains, don't try to immediately double-track your new network. More track = more cost. Keep it single-track with passing sidings here and there.
Once you have a profitable small network, expand by trying to re-use much of the original infrastructure. For example, if you started with the coal power plant, maybe you can deliver coal from some of those coal mines to nearby factories and have your vehicles re-use the exiting roads/rails you built. Then maybe use a lot of the existing network to also transport passengers. Eventually double-track parts of your rail network with the most volume of traffic.
Tip: Start off with Freight
For a really successful passenger network, you need many destinations to get passengers to where they want to go. I often do this by starting with freight first. Once that is profitable, I try to re-use as much of my freight network as I can to also transport passengers. Remember, building new track adds to your expenses. Once I've added passengers destinations and that becomes profitable, then perhaps I build passenger exclusive tracks to extend the network or improve the existing.
Tip: Avoid Lengthy Tunnels, Elevated Ways and Bridges Early in the Game
As I mentioned previously, tunnels, elevated ways and bridges can cost much more that regular roads/rails. Try to minimize building them early in the game.
Tip: Build Mostly Single-Track Railways First
I've already touched on this, but it can be important to control costs early in the game. Don't immediately try to double track everything. A completely double-tracked railway costs twice as much as a single-tracked one. If you do have to build a long bridge/tunnel, instead of two spans build one with a passing siding before/after.
Tip: Use the Finances Button
Use the Finances window to keep track of your costs. There are two main tabs, "Years" and "Months" which changes the time-span of your overview. The "Maintenance" line shows how much you're paying per month/year on those monthly maintenance costs. If you click on a category, it will plot those expenses/profits over time.