You don't pay any tax on dividends from shares within an ISA.
Outside an ISA, from 6 April 2016, you won't pay tax on your first £5,000 of dividends in the tax year. However, beyond £5,000, you pay tax depending on your income tax band. Basic rate tax-payers pay 7.5%, higher rate tax-payers pay 32.5%, and additional rate tax payers pay 38.1%.
If you use your Stocks and Shares ISA for interest-bearing investments, such as corporate bonds and gilts, the interest is entirely tax free. £10,000 invested in bonds paying an average interest coupon of 4% would grow to £21,911 over 20 years, assuming no fall in capital values and coupons are re-invested. The same amount held outside an ISA, and subject to additional tax payers rate of 45% tax, would be worth £15,453.
Any gains made by investments within your ISA are not subject to capital gains tax.
For most people, income and capital gains from ISAs do not have to be reported on your tax return. Nutmeg will send you a Consolidated Tax Certificate at the end of each tax year.