Hi Leor,
well, tl;dr :-), but I do support doco's answer. Spend some time and search this forum thoroughly, most answers will be clear after that. I suggest air travel may be the cheapest, not knowing where you live I'd suggest Lisboa-Frankfurt for starters, should be the cheapest. Maybe Interrail may be an option for rail travel. Best: team up with some furs and share a car. Roadtrip, yay! Or long-distance coach.
For accomodation check hrs.com, and google. On a budget: youth hostel (about 20 seconds from the maritim) or airbnb.de, if you dare ...
hugs
Ragear