We are taught to never give up on praying to Hashem, even though we don't necessarily get our prayers answered right away. No prayer goes unanswered. Hashem hears everything, He may not grant us our wishes because they are indeed not good for us. We think we know better than our Creator. Even though our prayer is always heard, even though the prayer may seem lost, it is not, as it may also benefit others.
Our Rabbis have taught that if you want something so badly, it is better to pray for that something for somebody else who wants it as well, not for yourself. The one who prays for others gets his prayers answered first. In addition, you can have someone else prays for you for the same thing. I've never been involved in this type of arrangement, so I wouldn't know. But there has been stories that this system works for some.
The goal of prayer is not simply to ask Hashem of our needs, really. It is to get closer to Hashem, to understand His Ways, to be one with Him while seeking the good for Am Yisrael, as we daven together for the needs of the Klal, as a collective.
I find the Siddur to be a very powerful tool to understand Hashem, learn about the halachos of davening, connect to Tehilim much more deeply, and learn Hebrew vocabulary! It takes me about one hour to finish Shacharis from start to finish (except for the formal Torah reading on certain days, as I don't daven in shul in the mornings, only privately). I really appreciate the Siddur even more after I've taken upon myself the importance of each different facet of Shacharis.
To learn from the Rav Meyer's class on Sefer Shmuel, go here.