While I can’t tell you how to pray to God, I can inform you how most Hindus perform puja and aarthi at home. How you pray and what it means to you should be entirely between you and God.
Most practicing Hindus perform puja anywhere from three times a day to once a week to only on holidays, depending on the devotion of the Hindu, as well as their preference in time of day and need of prayer. The Hindus that pray thrice a day do so once in the morning after waking up and bathing (but before eating breakfast), once at midday (after briskly washing the face and hands and before eating lunch) and lastly at night (after a quick wash and before eating dinner). We refrain from eating at least a few hours before performing puja so as to offer the food we are about to partake in firstly to God, and then to ourselves. It is also very important in Hinduism to be clean; not only for prayer but to make it a habit of washing the self throughout the day before we eat.
For the puja, we firstly need a few items.
One is a picture, statue or image of God. This is called a murti. Make sure the murti is made of some material (or covered in some material) that is appropriate to get wet and receive kumkum without staining. You can have as many murti as you like of whichever facets of God you choose.
Second is a raised table or stand. Something to put the murti on that is at least a little above floor level. Third is a nice cloth of your own tastes to place on top of the platform and under the murti.
Fourth is a medium-sized tray, one that is easy to carry but strong enough to hold items. This is called a puja thali and you can find many cheap and beautiful ones online.
Fifth are the items you will utilize for invoking God. These are candles (or diya lamps made of cotton wicks and ghee), bells, incense, kumkum, water, flowers/garlands or whatever food you wish to offer to God (optional). Place these items on your thali. Some also choose to dress their murtis in clothing or cloths or adorn them with red and saffron string called kalava (but most choose to tie kalava on special pujas or holidays).
To initiate the puja, light the candles or diyas start the incense and chant an invoking prayer while ringing the bell around your murti. The puja ceremony is basically an act of inviting God into your home, caring for them, praising them and setting them off again. So when we ring the bell, light the lamps and start the sweet incense smell, we are symbolically guiding God to our altar and allowing Him/her to sit on our presence. Once God has ‘arrived’, we wash the murti with water either all over or specifically on the feet and forehead to cleanse them after their journey to your home. If you wish to offer food, do so. Then we apply kumkum to the forehead of our beloved God and if you wish, then to ourselves. Adorn God in garlands or offer flowers on your thali. While doing so, you may chant your favourite mantras or praises to God. We then start aarthi, or the singing of bhajans (devotional songs) while waving your thali in a circle around the image of God. This can last as long as you want. Thirdly, we bow our heads and place our hands together in anjali mudra. Use this time after aarthi to pray either silently or out loud for whatever you wish. This is your personal and private time between you and the Lord. After you have finished, ring the bell again to let the Lord know it is fit for Him/Her to ‘leave’ your altar. Many say a praising mantra as they leave. Blow out your candles and wave the smoke over the murti and over your own head. The puja is now over.
I hope I have helped you and many others that may be wondering about how to perform the common puja! Please keep in mind though that these are all loose ‘rules’ for doing so, while many keep the same method, some things are changed around or added depending on the type of Hindu or the region of India that they learned their practice from.