Present time
Kavanah, translates as ‘direction’or ‘intention’, and is an important part of prayer, implying, where you are going, what is your direction and begs the question as to whether your mind is full of irrelevant thoughts. I.e. poor kavannah.
New to prayer
Someone who is new to prayer, particularly Jewish Prayer, could become quite distressed by the speed at which the prayers are recited, whilst simultaneously carrying on a conversation in sign language with a neighbour. During large parts of the prayers, speaking is prohibited, so intermittent brief communications take place by grunts and sign language. During meditation one also has conversations with various people.
Awareness
The solution to the dilemma is the same in both cases but is easier said than done. The solution is to pay attention to what you are doing.
In meditation one needs to be attentive to the breathing or any other part of the discipline one has been instructed in. In prayer it’s a little more difficult, because of the absence of clear instructions. There is a lack of clear understanding of the aim of prayer and even less understanding of the benefit.
Regarding prayer, one hears instructions to understand the meaning of all the words, but then you would not be able to continue at the breakneck speed of the congregation. Nevertheless you are paradoxically encouraged to continue at your own speed . Even when you understand the meaning of the words you still have to work on getting the sense of the prayer.
Stages
Just to find yourself holding a prayer book, a siddur, is already a major step . Why, because it is a step in acknowledging that there is something more to life than just the physical. It is a step to the thought that there might be a spiritual dimension worth exploring.

An important aspect of the prayers, at their lowest level, is that they are methods to bring you into present time (See Present time). Anything that takes you away from narcissistic, egotistic, mind wandering during prayers is legitimate. There are a number of methods to do this

Just reading the words, with attention, kavannah, is a big and important step. This takes you away from distracting thoughts
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Reading the words as above, but softly sounding them is another step.

Instead of reading, try singing gently and softly. Most likely, you don’t have a tune, make one up then or listen to the sing-song tune of others who sing. The benefit of singing is that it activates the right side of the brain which is connected with art, music, space, intuition (See right brain)

You can of course also try to understand the meaning of the words of the prayers.

You can connect with the feelings of longing and love to be closer to the divine. Read Solomon’s Song of Songs.

During the parts of the prayer recited by the Chasan ,one can practice simply being aware of the place or room with the other people in it. (see makom). One can in fact also just be in the synagogue absorbing the rich atmosphere. There is a story of the Baal Shem Tov in the synagogue when a peasant farmer unable to read was overwhelmed by the service and started loudly crowing like a chicken rooster. The Baal Shem Tov stopped the gabboim trying to throw the man out, explaining that this was his way of expressing his religious fervour and participation with the prayers.

During the repetition of the 18 blessings, the Amidah, you can listen and answer OMAYN. This, in itself, is not only your contribution to the community, but also takes you into the mystical realm of sounds and vibration (See Vibration) and the connection with the other chants like the Hindu OM (See Omayn and Om)

As you can see there are many areas in which to exercise your awareness or consciousness.

Why pray?
Look for the magic of the prayers that keep people coming year in and year out, rain or shine. What are they getting out of the prayers that keep them going with such fervour, despite their poor kavanah
The answer could be the atavistic, ancient need for men to band together for protection and food, or it may be because of the special presence of the shechina, or it may be the power of the letters them selves that sooth and energise. Or all together. The power of the letters on the physical body can be demonstrated by applied kinesiology.
Chanting

Chanting is also part of prayer which you can do at any time.

1 Mode .................I..am, in gratitude.

2 Ani ....................I or me............................. Ayin........... nothingness

3 Lefonecha .........before You. Hashem....... Ein Sof........ vastness without end

Mode Ani, is the first prayer in the siddur. It is a chant one can learn by heart, and is recited first thing in the morning when one realises one is awake. This is an opportunity to thank the Divine for giving you another day of life. A powerful example of Ayin and Ein Sof.

There are stories of men fainting when they recited this prayer, because sometimes they were so overwhelmed, addressing the divine so early in the freshness of the morning

In conclusion it is good to bear in mind that the principles of meditation can be applied to most actions, non more so than prayer