Prayers according to Sunnah
Although one should pray to Allah at all times for all one's needs, our eternally blessed Prophet has taught us some specific prayers for special occasions at different times of night and day, e.g. upon waking up, when going to the toilet and coming out of it, when performing ablution, upon entering and coming out of the mosque, upon entering the house, before meals and after, after hearing the adhan, when dressing, when looking in the mirror, before falling asleep in bed.
Tt,ese prayers are all-embracing and extremely useful for all our worldly and other-worldly needs. We by ourselves can never think of such prayers which the eternally blessed Prophet has taught us. These prayers are not time consunung nor ablution is their precondition nor is one to raise his hands. If one commits them to memory, one reaps a very rich harvest both here and in the Hereafter.
Hence every Muslim must commit these prayers to memory. There are many books wherein they are listed. Maulana Ashraf Ali Thanvi's "Munajat-e-Maq-bul" has most of them. You should commit them to memory and ask your children to memorize them too. These shall earn great merit for you.
Praying for others
One prays for one's own needs and desires, but one should also pray for one's relatives, friends and Muslims in general as it is an act of great merit. There is a hadith which says that when a Muslim prays for anyone of his brothers in faith in the latter's absence angels pray for the same for him (Sahih Muslim).
Hence if you come to know that any Muslim is in trouble or need, pray for him. In fact one should pray for the unbelievers too so that they may be Divinely guided on to the path of Islain. Thus one gets merit for the act of praying as well as for wishing well for others.