Ever since the year 800, when the Council of Rouen forbade the lay faithful from receiving on the hand, reception in the mouth has been the traditional way to receive Holy Communion. Of course, now it is perfectly legitimate and fine to receive either on the hand or on the tongue, either standing or kneeling.
If you wish to receive on the tongue, after you say "Amen" open your mouth and raise your head a bit - just enough for the priest to see what he's doing - and stick your tongue out a bit, so he can place the sacred host on top of it, rather than having to introduce it inside your mouth. See a picture of Mother Teresa here.
I believe it is still in the Roman Missal that we are supposed to employ communion patens to avoid the risk of the Blessed Sacrament falling on the ground. Unfortunately this is barely ever done. Therefore the best position to receive on the tongue remains kneeling. In that case, stay a few steps back from the person in front of you, and when they walk away, walk forward and kneel immediately but gently, as the priest starts to say "The Body of Christ". After kneeling, say "Amen", and then do as above, but raise your head a little bit more.
This is how I and many people I know ordinarily receive Holy Communion in the Ordinary Form of the Roman Rite. And we also prefer reception from a priest or deacon, since EMHC should only be employed when strictly needed because of a shortage of priests or deacons, and this is not often the case.
For the other questions: never say anything after you receive the holy Eucharist. In the Ordinary Form you say "Amen" before you receive it. In the Extraordinary Form you do not say a word. Once you receive the sacred host, you may chew it. It is perfectly respectful, surely the priest himself does so, and it will also avoid inconvenients such as the species of the bread sticking to the top of the mouth and distracting us from the prayerful contemplation of the Divine Substance.
You do not have to make the Sign of the Cross afterwards, but you may, if you so want to welcome the good Lord in your heart.
After Holy Communion, you are a living tabernacle for about 15 minutes. Unfortunately, not many take notice of this and often leave way too quickly. The Lord has mentioned this sad circumnstance in several private revelations. Therefore, remain in quiet recollection even for 10 to 15 minutes after Holy Mass has ended, and the Lord will be very glad of this time you are spending with Him.
St. Padre Pio used to describe Holy Communion as "a fusion, like when two candles melt together". Such is the greatness of this Sacrament most Blessed, of the consummation of this mystical matrimony. Some saints recommend to pray to Our Lady to be in our hearts, so that the Lord may dwell in her beloved Mother (His most exhalted throne of glory) all the while he dwells in your heart (His favorite temple).
Some have written that we should focus above all else in thanksgiving when we have received Holy Communion. Of course, when Christ is one with you, you may bring any matter to His most loving attention, or even none at all and just love Him for a while. But to simply spend that time of heaven on earth making requests is not the most perfect way to go.
Love the Eucharist, always remembering how wonderfully it embodies the words of the Holy Spirit:
Do not fear, daughter! See, your king is coming, meek and humble.
For if you could see the Lord in His glory, without the veil of the Bread of Life, surely you would die of sheer joy and awe.