Kavanah whilst Davening

In general, when performing a mitzvah one must have intent to fulfill that mitzvah (See Having Kavana for Mitzvot). Additionally, since one is reciting brachot when davening he must also ensure to have all of the proper kavanot when reciting brachot see Kavana During Brachot.

There are specific additional kavanot (intentions) one should have that are unique to davening:

Proper Frame of Mind for Davening

1. One should not pray while one is in the state of sadness.
2. One should not begin to daven while in a state of laughter and levity; rather, one should enter davening with a state of seriousness ("koved rosh").
3. One should begin to pray with a sense of happiness for the mitzva he is about to fulfill similar to the joy one experiences when one is involved in the study and pursuit of Torah knowledge. This is why we recite Pesukei DeZimrah and Ashrei (words of Torah) before beginning Shacharit and Mincha.

Bringing the Proper "Korban"

1. Chazal tell us that "regardless, if one brings a large korban or a small one as long as one's intentions are for heaven (one's korban is accepted)." The same idea applies to Tefillah.
2. Accordingly, if one can pray a lot with Kavana or a little with Kavana, clearly it's better to pray more. However if there are extenuating circumstances and it's not possible to pray a lot with Kavana or one judges that if he prays more he'll pray without Kavana, one should pray less with Kavana rather than more without Kavana and it's considered before Hashem as if one prayed a lot with Kavana.