In summary, for normal people, taxes in the US come at federal, state and local levels.
1. Federal:
a) Income tax of 10% on income over around $12k (single) or $24k (married) up to 37% on income over $518k (single) to $622k (married). Capital gains tax is at the same rate for assets held less than a year but up to only 20% for assets held more than one year.
b) FICA, a wage tax. You pay for 7.65% for social security and medicare/medicaid on all wages up to around $133k and 0% above that.
2) State. This varies widely. Some states have no income tax, some states have income tax rates of as high as 13.3% (California). Most are around 5%. Each state has different deductions and rules. Capital gains is usually included in this. Most states (but not all) also levy a sales tax of around 4% to 8% on retail transactions.
3) Local. Most local taxes are in the form of property tax on real estate. The rates vary from around 0.5% to 2% of property value. Some towns levy a separate sales tax on top of a state one (if it exists). The real estate and sales taxes are used to fund schools, police, fire, etc. Many municipalities also levy fees for water, trash, etc. Some cities also have an income tax (for example NYC).
To give you an idea of just how complex it is, the US has approximately 11,000 different sales tax jurisdictions. And it's not just a matter of rates. What is taxed and in what context varies. For example, in NYC, food from groceries is not subject to sales tax. But food from restaurants is. Unless, I think the restaurant has no more than some minimum of seats and you orders your food to go. Some sales taxes can also vary by date (i.e. sales tax during summer, but otherwise none). There are also occasional sales tax "holidays" where no sales tax is charged.
Unsurprisingly, tax lawyers and accountants make good money in the USA :-)