To take His yoke is to submit to His authority, His right to rule and to be Lord of your life.  To learn from Him is a call to discipleship.
Before Jesus ascended into heaven, He said these words:

Matthew 28:19-20
"Go therefore, and make disciples of all nations, baptizing them in the name of the Father, and the Son, and the Holy Spirit: Teaching them to observe all that I commanded you ..."

Jesus is clear on what it means to be His disciple.

In Luke 9:23-24 He said,  "... If anyone wishes to come after Me, he must deny himself, and take up his cross daily and follow Me.  For whoever wishes to save his life will lose it, but whoever loses his life for My sake, he is the one who will save it."

In Matthew 10:37-39 Jesus says, "He who loves father or mother more than Me is not worthy of Me; and he who loves son or daughter more than Me is not worthy of Me. And He who does not take his cross and follow after Me is not worthy of Me.  He who has found his life will lose it and he who has lost his life for My sake will find it."

To lose your life for Jesus' sake means: giving up your life and embracing His.
Luke 14:25-27
Now great multitudes were going along with Him; and He turned and said to them, If anyone comes to Me, and does not hate his own father and mother and wife and children and brothers and sisters, yes, and even his own life, he cannot be My disciple. Whoever does not carry his own cross and come after Me cannot be My disciple. 

Here, Jesus is not advocating hate but emphasizing contrast.  Not that you are to hate your father or mother, etc. but that in contrast or by comparison the love you should have for Jesus should be so much greater than the love you have for others that your love for them would almost seem as hate.  (true love for others only comes from loving Jesus the most)

Having said that - Jesus made hard demands, impossible demands, to say the least, of what it means to be a disciple/a Christian. There is no separating the two.  To be a Christian is to be a disciple and to be a disciple is to be a Christian.  They are one in the same.  (There is not two classes of believers)

The demands Jesus made to be a disciple are impossible to achieve without God and that is exactly why we cannot compromise the demands of the true gospel and change them to the point that a man can seemingly accomplish salvation in his own strength; thereby, resulting in a false assurance of salvation. For when we change the message, no matter how well meaning the intentions or how noble the cause, it ceases to be the Gospel of Jesus Christ, and can only create false converts. Let us not forget, salvation is only found in the true Gospel of Jesus Christ, not in the opinions of men.

In Mark 10:26 we find the disciples questioning who can be saved and in Mark 10:27 Jesus replies, "With people it (salvation) is impossible, but not with God; for all things are possible with God."