Trade tariffs are complicated, and it is the legal responsibility of importers and exporters to apply the right tariff to each transaction.
Here's more background than you could possibly want
https://www.gov.uk/trade-tariff/sections
At the moment, tariffs within the EU are zero for most things. If the UK leaves it will no longer benefit from that zero tariff regime.
In all likelihood, the EU will charge a 10% tariff on stuff from the UK since it will move from the "in the EU" column to the "out of the EU" column and therefore a different tariff rate automatically applies. Some types of product or service may incur tariffs much higher than 10% - again, the processes are already in place and apply to hundreds of countries (they'll simply apply to one more if the UK leaves)
Similarly, the UK will charge a tariff on exports.
This will make the UK's exports more expensive and therefore less competitive with EU producers, and it will make everything the UK imports from the EU more expensive (helping local UK producers, but in many instances there are no suitable UK alternatives since the industries in question have pretty much died out)
All this can be changed post-facto through negotiation, but that's on a product by product, industry by industry basis.