What is the best way to learn tones?
All the 5 tones in Mandarin exist in English already, but not used in the same way.

1st tone:  I am a STUUUUU-dent. 

When you read this sentence in the normal way, the syllable STUUUUU carries the first tone.

2nd tone:  Are you a stu-DENT?

When we ask a yes-no question in English, we need to raise the last syllable of the sentence. The syllable of DENT? carries the 2nd tone.

3rd tone:  

Your friend tells you an unusual story, and you are surprised, and you ask in surprise: REA-ly? in the way that the syllable of REA goes down, and the syllable of ly goes up. In this case, the syllable of REA carries the 3rd tone, and ly carries the 2nd tone.

4th tone: pay lay day lie pie tie buy my high (Those words, when read alone, carry the 4th tone.)

Another example: you accidently hit yourself on a corner of a table, it really hurts, right? So what do you say? You say: Ouch!, which carries the 4th tone.

5th tone (the neutral tone): Go A-head.

The schwa A carries the 5th tone.

See this video for the tones: Mandarin Made Easy

From my Mandarin teaching experience, I think mastering the 4 tones individually is easy for English speakers, but consciously applying the tones on each syllable in Mandarin is very challenging for English speakers, because tones are not used in English in this way.

You can practise tones by reading the following sentences aloud. You may have already noticed that all characters in each sentence have the same tone.

1st tone:  今天三家三星分公司开张。

2nd tone:  德国游人年年来长城游玩。

3rd tone:  祖母总给予我理解与鼓舞。

4th tone:  第二次世界大战正在迫近。

If you can read aloud those sentences correctly without any hesitation, then you know you have won the battle with tones.