To make easy money at the very begining of the game (mission) search for towns that have production facilities (farms, loging etc) and in the same time need that resorce (for instance town has logging and in the same time requires logs).
Buy a lot in that town and build a warehouse on it. You can than using the warehouse buy logs from logging and sell it at triple price to town.
You don't need to have a railroad line to that town. Do that in 5 to 6 towns and you are set with money for the duration of the mission.
Remember to cycle through your warehouses every month or two as towns develop needs quickly and you can make some easy money.

If for some reason you can not build a warehouse in town that needs the goods which itself produces you can always build a railway line to that town and park a train (locomotive) in it's station.
The locomotive than acts as a warehouse only with less capacity (2 -3 instead of 20 -30).
To make money just load the goods from production facility to train and unload them to city hall or factory. The process is nearly instant, the train does not go anywhere and you have tripled your money.
In order for this to work give train first the order to load the comodity only. When train is loaded delate that order and give the order to unload only. When train is unloaded delate that order and give the order to load only. Then again delate and unload. You can repeat this steps as long as you wish.
Remember to do this every month or two and you are set with money.

Important: You can use the railway lines and stations of your AI competitors in single player mode. Just conect to one of his stations and you have access to his entire net. It must be done at the very beginning while his stations still have free connections.

The best way to make money is to use the global market (commodity exchange).
At the very begining of the game pause the game and build a trading department in your office.
Then search for cities that have vacant lots. Your aim is to create trading chains. Trading chains are for instance oil - rafinery- city that uses kerosine or logging - saw mill- printing press/city that uses paper or lumber. When you had find all the links in a chain and they all have vacant lots build warehouses in those cities. You can now manipulate the prices to your advantage. It works like this: If you need cheap cotton for textile factory and the cotton is expensive on global market go to your warehouse at cotton farm and buy cheap cotton from farm which you than sell at higher price on global market. That will push the prices of cotton down. Than go to warehouse at textile factory and by cheap cotton on global market and sell it at higher price to textile factory. That will push the price of cotton up. Than go again to your warehouse at cotton farm and repeat the whole process.
Your aim is to make 500 to 1.000 (sometimes it can be 7.000) per transaction. It can be done with all tradable comodities.
Frequency of trade matters. It's like they told you at school "Buy cheap and sell high".
You don't have to build a railway line to cities with vacant slots in order to build a warehouse.

I hope that this will be of help.