The Trams and the Metro are fast, easy and very unintimidating for those who didn't grow up with a metro system. So dont be afraid, give it a try.
The Trams and the M1 in particular actually add to the experience of being in Budapest and in no time at all you will feel like a local as you move around town.
So, I am always telling people the first thing you do is find a ticket window or ticket machine or information office to purchase a TravelCard for 24 or 72 to Week long use. They are inexpensive and because the whole system works pretty much on the honor system, you just carry it and show it when asked.
So the purpose of this post is to suggest an alternative to the paper tickets. Download "BudapestGO" on your phone and you can buy your TravelCard on your phone and plan your routes. Pretty slick App.