Despite having been formally taught Chinese in school by some fantastic teachers and professors, my first few experiences in China were met with wayyyyyy too much frustration. If you are a foreigner who has studied Chinese, and have ever been to China, you will probably have run into a similar situation. You have proudly just responded to a question in Chinese, feeling good that you were not only able to understand the person who addressed you, but also that you were able to respond in such a fluent manner.
Except that proud moment was just that: a very, very brief moment. You just completed your sentence with a smile on your face, when you are responded to with a look of puzzlement and a 听不懂 (ting1 bu4 dong3 or if you're in Beijing ting1 bu4 dong’r3). No possible response could give you a more belittling feeling. All that progress you thought you had made, only to hear that you are incomprehensible to native speaker.
As a student of Chinese for over eight years, I've come to appreciate the difficulties of the Chinese language. One of the most challenging aspects of Mandarin is definitely tones (disclaimer: while my pronunciation is not perfect it is getting pretty close). In Chinese class, our teachers would drill us each and every day, and my classmates and I would always struggle with one tone in particular: the third tone. Why is it so hard? Our teachers told us that we were supposed to pronounce it by going down a little, than up, as shown in the graphic below.
The concept seemed easy in practice but yet when talking with Chinese people I would often hear a 听不懂（ting1 bu4 dong3）or “I don't understand” when I was simply trying to express that I was an American， 我是美国人（wo3 shi4 mei3 guo2 ren3）. After many years of feeling ashamed of my poor Chinese where I couldn't even tell somebody where I was from, I finally had one Chinese teacher try to explain things in a different way. Instead of dropping down before coming back up, I was told just to go down and hold. See the picture below for details.
She said that almost every foreigner she has taught ran into this issue, and that often non-native speakers’ overcompensation on the rise of the third tone made it seem as though we were using the second tone. Usually if somebody drops down and holds as the picture shows, they will subconsciously rise back up anyways and it will sound natural to a Chinese speaker. So try this out and see if it works! Then you can practice this funny phrase that same teacher taught us to practice our transition between the second and third tones: 美国女人有钱 (mei3 guo2 nǚ3 ren2 you3 qian2 : American girls are rich).
Try some of these other phrases:
怎么可能?! (zen3me ke3 neng2: How is this possible?!)
买单。 (mai3 dan1: Check please!) Very practical for eating at Chinese restaurants
我喜欢吃水果。（wo3 xi3 huan chi1 shui3 guo : I like to eat fruit)
It is important to remember that in cases where you have two third-tone words next to each other, you should pronounce the first of the two words as though it is the second tone. So this sentence should actually be pronounced wo2 xi3 huan chi1 shui2 guo3.
Another example along these lines is that 你好 (ni3 hao3 : hello) should actually be pronounced as ni2 hao3.
As always however, the best way to learn a language is to talk with native speakers. Naturally I recommend that you sign up to practice with some good teachers. Two of my favorites are Christine and Zhangdong. I think with Chinese particularly, it is important to get exposed to as many different speakers as possible, as regional accents differ quite drastically. Considering over 1 billion people worldwide speak Chinese, you will want to be able to understand more than just one of them!