Trading has gotten a lot cheaper and more accessible over the years, so that even people like you and I can make investments without getting eaten up by fees. Still, most people don't even realize that they're losing money to these things.
Commission
This is most likely the largest portion of costs for most people. If you trade in $1000 positions, and each position costs $8 to put on, then you're paying 1.6% to enter and exit each position. This may not sound like a lot, but depending on how often you trade, it does actually add up to a huge amount. Try to find the cheapest brokerage you can.
Taxes
No idea what laws are for other countries, but in the US, you're taxed on your ordinary tax rate for positions that you hold for less than a year. On the other hand, losses can be deducted. For positions that you hold for more than a year, there's a lower, capital gains tax. It makes a pretty big difference, so do your research.
Fund fees and expenses
If you're interested in mutual funds and ETFs, it's important to check how much the fund takes out in expenses and management fees. Morningstar is a good place to look stuff up. Depending on how long you plan on holding it, something like 1% a year really adds up over time.
Bid-ask spread
Let's take Citigroup (C) as an example stock. Say it's trading at 4.11-4.12. That means you can buy at 4.12, but you can only sell it at 4.11. That's a penny loss, which comes out to about 0.24% in this case. It's minor but relatively important to keep in mind for less popular things. The spread can be much wider, especially if you're putting on a larger position, and you should definitely think of that as a cost.