You have three main choices:
1) You open a taxable account with money that was already taxed. You do this by going in person or online and buy stocks with money in your bank account. When you open the account, you tell them that it is not a retirement account. Your gains will be taxed (but not the original money since it was already taxed). For example, if you put in $5000 and eventually it is $8000, you would owe tax on that $3000 difference. But if you hold them long enough the tax is often quite minimal. With dividends, you owe the tax the year the dividends were paid.
2) You open a retirement account with money that has already been taxed (by purposely signing up for some form of an IRA on your own). In this case, you never pay a penny of further tax as long as they are US stocks. You probably will pay a bit of foreign tax if they are foreign stocks, but the company that you buy the stocks from will take care of all that for you.
3) You open a retirement account with money that has not yet been taxed (through your work with money that they would otherwise pay you). You never get the money from your work, so you don't pay income tax on it (yet). In this case, you pay tax on the original money when you withdraw it in retirement.
Usually people reinvest the dividends. That is one of the two ways that you make money in stocks. Either the stock goes up in value (usually exponentially), or the divends go up in value (usually exponentially) if they are reinvested. If you don't reinvest them, then the dividend is just a one time shot of cash - nice to have but nothing spectacular.
The case against reinvesting dividends is that you are now buying stocks that you might not have wanted to buy. For example, suppose you have too many large companies in your portfolio and not enough small companies. If a large company pays a dividend and it is reinvested into that company, you just bought more of that large company. That could be the opposite of what you intended to do. You basically lose a bit of flexibility with reinvested dividends.
If I were you, I'd reinvest them.