Many people are misinformed concerning contemplation.
I will try to keep it simple.
There are 4 kinds of prayer: vocal prayer (Our Father, Divine Office), meditation or mental prayer, aquired contemplation (prayer of simplicity) and infused contemplation (which is a mystical prayer).
Every Catholic can learn to pray vocally and to meditate. For spiritual growth, meditation is very important and spiritual writers recommend it to be practiced daily for at least 15-30 minutes (if one can manage to meditate more, that’s great). Meditation actually consists in reflecting on a truth of faith (one can read slowly a Bible chapter or some spiritual book) and then making some spiritual acts - act of faith, love, humility etc. For example, you read about Jesus’ passion and then say: Jesus, thank You for saving me, I love You, I repent for having caused You so much pain by my sins.
When one practices meditation faithfully for a long time (maybe for a few years), one’s meditation becomes simple - this is aquired contemplation. It does not involve much reflection as before, and sometimes only one thought can elicit spiritual acts. Also, acts become less numerous; one act, for example an act of love, can last much longer than before. For example, a person can remember Jesus’ passion and then make acts of love for a longer time (repeat Jesus, I love you, and feel as if no other words are necessary, this act alone makes soul content in prayer). This doesn’t mean that this person doesn’t ever meditate or pray vocally. Rather, it continues meditating when it cannot pray in this way. This degree of prayer is still not mystical, but can actually be achieved by one’s “efforts”, of course not without the grace of God (but only if a person has been faithful in meditation for a while or if it can pray easily this way…anyway, a good spiritual direction would help).
Infused contemplation is a mystical prayer which cannot be learnt or achieved by our human efforts. We can only be faithful to God, desire holliness and persevere in meditation and battle against sin. When God wills and if a soul is prepared, He can give Himself to her in this mystical way, and that’s real contemplation. Soul is here passive, which means that it cannot start to pray this way by her own effort. Beginnings of infused contemplation happen in the dark night of senses.
I hope I clarified this well. I am not a theologian, but I read a lot on this topic. Maybe my explanation of aquired contemplation was too simplified, so I recommend you reading more on internet, but find good and checked resources (there’s an article on New Advent on contemplation, try to Google it).