The short answer is - you can't do an expedition. It takes lots of time, money and effort to organize an expedition and requires experience.
Your best bet for visiting the Arctic (anywhere above the Arctic circle) would be to either fly or drive. You can fly to Barrow, Alaska, or you can fly into Norway, Sweden, Denmark or Russia and then drive to Arctic communities with no problems at all. There are cruise ships that visit the Arctic too (though maybe not at the moment with Covid-19). You could also fly to somewhere like Greenland potentially, but I think it would be boats from the towns to the Arctic.
If you are serious about an expedition - this is something that takes a lot of time, planning and last but definitely not least, money. We are talking cost per person in the $50,000-100,000 or more sort of range. It involves transport, food, shelter, clothing, equipment, where exactly, when exactly, how many people, weather, etc. It also generally requires experience - this is not something you can just do without any out-door experience at all.
So - with no experience how would you go about this?
Well, the answer is to start - go camping first off (maybe you'll hate it) - try your local forest park. From there, go hiking on trails. Then with time and experience, go hiking off trail and at different altitudes for longer and longer times (days/weeks). Then, with more experience, try camping and hiking in the winter with snow and ice. Learn to navigate by map and compass in the hills, learn snow/ice techniques, first aid.
Once you have a start on those, you might be able to consider planning your own expedition - but to get the money you generally need sponsors (like your favourite sports star has) - which means you need a goal - so what are you going to do, that will impress people enough that they will fund you?