There will be an array of consequences, some of them beneficial others not so good. The most severe effects will be felt by the underdog in first instance, from travel, through education to taxes. Below is a summary of what we know so far. 
Taxes and Trade

Zero taxes, no tariffs on trade, we know it will translate into everything in our lives, the more expensive taxes the more goods and services. Zero taxes means we will not have to pay any additional money on top of what we already take advantage of that comes from the Union. Access to employment will be more stringent because of the disappearance of automatic recognition of professional titles and professions.

Law 

As a member state of the EU, Great Britain had an advantage of having access to a central criminal database. This does not mean that the UK will lose the intelligence which is crucial to national security. In addition, legal sovereignty of the UK was always subject to the EU law and our domestic law wes always subordinate, this is no more. This is good news for national purists because law will be made by the British, passed by the British and interpreted by the British. Checks and balances will be even more crucial now. There will be no scrutiny from the above and keeping in shape will require more discipline on the UK’s behalf.

Travel 

Only British passport holders will need a visa for a stay which is longer than 90 days on EU territory. In addition, European Health Cards will cease to be valid and therefore UK nationals visiting the EU will have to obtain travel insurance. Roaming will no longer be free and therefore communication over the phone outside the UK will be more expensive, this must be explored within each network separately. 

Citizens leaving for the EU will have to ensure that their passports are valid for at least six months. 

Education

EU students used to enjoy the same tuition fees as UK students, this will change from 1st January 2021. All EU students will have to pay the same tuition fees as all other overseas students and those fees can reach up to £40,000 on public universities. 

Fishing

There have been plenty of talks on this topic and right now EU boasts will be allowed to stay on UK waters until further notice, this means, years to come. Nonetheless, the UK now has its sovereignty and coastal independence restored. This is still to be negotiated for the next five and a half years and access to waters will be discussed on an ongoing basis.