Hi TINM,
Being baptized is a very important part of one's journey with Jesus. You are correct that Jesus seemed to be speaking of the very same water baptism that he himself received when he explained to Nicodemus that one must be born of water and Spirit. I would draw your attention to Jesus' baptism as an example of 'how' one should be baptized. It should be at the hands of another believer and by full immersion of the body in water.
John the Baptist had spent many, many days baptizing by the river Jordan and I'm pretty sure he picked that spot, or God led him to that spot, because that is how baptism is supposed to be.
As for the right time, well, when you have believed the truth: that Jesus died for your sins and on the third day was resurrected to life by the Father, then you should be baptized. However, don't let your walk with the Lord stop there. My encouragement is, and I myself followed this path, once you have believed the truth that you then sincerely and earnestly pray to the Father to give you wisdom and discernment through His word. That He give you an unquenchable thirst for His word.
If you don't attend a regular worship service, then I would encourage you to find a strong bible believing fellowship and talk to the pastor about being baptized. If that isn't workable, then there really isn't any command or instruction that a baptism be performed within the walls of a building. Find another believer, and I don't mean just some 'hail fellow go thy way' Christian. Someone that you truly believe and respect as a believer in the Lord Jesus and ask that person to baptize you. I would recommend a man since that does seem to be the example of the Scriptures. However, let me repeat, as a young believer, there are ravenous wolves outside of the flock, and even within, that will now try to tear you apart from your faith and you really should look for a strong bible believing fellowship with which to be a part. It is not good that we not join with others from time to time for refreshing and encouragement.