A lot of people all around the world have noted their observations as they started to learn Esperanto. Read for example what Marina Evdokimova, a 17-year-old girl from Russia wrote:

"I realized that it's actually not very 'normal' that I had been learning the language for just two months and already could express basically everything I wanted to, albeit looking up many words in the dictionary. I was so inspired that I read Gerda malaperis! to the end in three days :) Esperanto is addictive."

What others had to say:

Today I completed 6 weeks of learning Esperanto. I can't say that I'm fluent, but I can communicate easily enough (with a lot of help from the dictionary, of course!).
...
Now I'd like to continue my study of Esperanto and use this language for communicating with different people from different countries. I have used Esperanto to talk to people from places like Brazil, whose language I don't know. For me, Esperanto opened a window to another world and that's what I like most about the language. I have to confess that at some point I was curious whether it was a good idea to learn a planned language. But afterwards I became aware that to learn several languages is never a waste of time, especially if it helps you communicate with the world.
I hope that some day I will be able to fluently speak and write Esperanto, but first I hope that this message is at least half correct!
-- Shoma, India (text translated from Esperanto)

I'm still amazed how much I understand without too much effort. And I'm pretty sure I will continue with Esperanto after the six weeks are up.
-- Jeff Lindqvist, Sweden

I had a very negative attitude towards Esperanto. My feelings were, why spend time learning an artificial language that has no practical value when there are so many real languages out there that can be useful to learn.
Then I borrowed a book from my local library when I was giving a lecture on the easiest way to learn a new language and to promote my book. I found the book, Esperanto: Learning and Using the International Language by David Richardson.
I was intrigued. The book changed my mind and answered many of my unspoken reasons for not learning the language. I looked up Esperanto on Google and downloaded websites and free courses - especially from Lernu!. I already had the Transparent introduction to Esperanto on the 101 Languages program.
Now I have had invitations to correspond in Esperanto and I have been learning as fast as I can. The language is really easy to learn and I can correspond with Latvians and Poles who don't speak English. I don't think I could have learnt any other language as quickly.
-- Bill H., Australia

Esperanto sounds are not very attractive, but really easy to comprehend. I speak only one European language and am still learning a second, so I can't understand many word roots and have to remember many basic words by rote. Yet, the simplicity of Esperanto makes it possible for me, as a Chinese speaker, to learn so much of it in about 10 hours.
-- Xie Z. A., Hong Kong/China

So far the "komencanto" and "bildoj kaj demandoj" lessons of www.lernu.net have been very useful for me. I really have the feeling I'm learning really fast which boosts motivation. So far I've studied 5 hours in two days without a pain...
-- R. R., Netherlands

So, first thoughts on esperanto: Holy crap, it's easy!
Second thought: this experiment isn't really going to be that useful. Esperanto is obviously a Romance language, by vocabulary and grammar if not by genealogy. With my knowledge of French, I can trace the origin of maybe 90% of the words I've encountered so far, and my English and Swedish accounts for more or less all the rest. As such, learning Esperanto will be extremely easy for me, as compared to someone who doesn't know another romance language, so comparing results will prove very difficult. I've never studied a language closely related to one I already know before, I didn't think the carryover would be so big. It might (and probably will) get more difficult later, though. But at the moment, I almost feel like I know Esperanto better than Mandarin.
-- -- S. Pettersson, Sweden

I've been mainly relying on two language programs from Lernu.com, the ones featuring Zam and Ana Pana. I downloaded the pdfs and audio from the download section, and listened to the audio a couple times while reading the Esperanto text. After that, I read the grammar notes, then loaded the audio onto my iPod, and listen to each course completely at least once a day. I reviewed the text with the audio every couple of days to see which words I wasn't getting just from the listening. My comprehension is something like 70-80% now, because Esperanto is that d**n easy.
-- E.B.H. (after 2 weeks of learning)

Also read the detailed account of Chinese Esperanto speaker Zhu Xin at http://www.amuzulo.net/pekino.html .