When visiting shrines and temples, I often get confused on the prayer offering manners. It is quite alike at shrines and temples. Below is a quick simple explanation on the two different manners.
SHRINES A facility to worship the god of Shinto
First, bow once facing the main hall before entering the shrine gate, or “TORII”.
The wash basin would be your first stop. 
Please purify yourself by taking the ladle in your right hand to scoop a cup full of water.
Use one fifth of the water to wash your left hand and the same for your right hand after switching the ladle onto your left hand. Bring the ladle back to your right hand and drip one fifth of the water onto your cupped left palm. Use this water to cleanse your mouth and finally wash your left hand with the remaining water. Finally, place the ladle back so that the cup is facing upward. This way, the remaining water will drip down the handle and clean it.
Once you arrive at the main hall, throw a few coins into the offering box as monetary offerings. 
If there is a bell, you can ring it to before offering your prayer. It is meant to get the god’s attention.
Finally, time to offer your prayers.
Bow deeply twice, clap your hands twice and join your palms when offering your prayers. Lastly, bow once.
Before leaving the shrine grounds, bow again to the main hall before exiting the shrine gate.
TEMPLE Originally temples were homes of practicing Buddhists.
( “Oshakasama” is the Japanese name for Shakyamuni, the founder of Buddhism. )
Before entering the temple gate or “SANMON”, place your palms together and bow once.
The same process for purification at the wash basin applies here and the procedure would be the same as when visiting shrines, as above.
Although many temples do not allow the general public to ring the bell, if there is a notice permitting this, feel free to do so. It is meant to get the attention of the gods and inform them you have come to visit.
If there are incenses or candles, make offerings using these steps as follows.
First, purchase incense or candles by paying the designated cost. Some temples do not set a cost and instead, accept the amount you feel fit to pay for these.
If offering candles, only one should be lit. Some sectors designate three for number of incense, but if it is not specified, one should be good enough.
Enter the main hall and throw a few coins in to the offering box as monetary offerings.
Place your palms together and bow once at a 45 to 90 degree angle. At this time, offer your prayers. There is no hand clapping at temples as compared to shrines. After you are done with your prayers, bow lightly before leaving the main hall.
Before exiting the temple gate, face the main hall and bow once.
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