Q. Do I pay taxes on investments?
A. Simple answer: no. That is, you do not pay income tax on the increase in value of your investment. What you have is an "unrealized" gain.
You pay tax when you realize that gain (or loss). That is, when you sell some of your investments. You will also pay tax if you investments that pay any interest, dividends or capital gains distributions.
The good news is: if you have any taxable activity, in your investment account, the account manager will report that to you on an IRS form. 1099-B for capital gains/losses on sales. 1099-Div for dividends or capital gains distributions and 1099-Int for interest.