After entering the temple grounds, you can just look around and leave. However, there are a few more things you can do if you want to do a proper omairi. There is usually some kind of water facility for symbolic cleansing. Usually, it is some kind of pipe, often decorative, delivering water into a large basin. There are usually long-handled ladles on the rim of the basin. In places where crows or other birds are a problem, there may be some kind of mesh or other protective materials that you need to work around. Anyway, most of the explanations of the procedure suggest you take the ladle in your right hand. Take a dipperful from the basin and kind of swirl it as you pour the water on the ground near the base of the basin. (Be careful not to splash your neighbors if the situation happens to be crowded, like at Sensoji.) This is symbolically cleansing the ladle. Then, hold the ladle under the spout of the pipe to get the purest water. Pour a bit of water over your left hand, while you rub your fingers together. Shift the ladle to your left hand, and repeat the process, cleansing your right hand. Then shift the ladle back to your right hand. Pour a bit of the water in your left hand and bring your hand up to your mouth. Since it is only symbolic, it is not necessary to put the water in your mouth. * Some people take water directly in the mouth from the ladle. This is not recommended! * Then, take one more dip of the ordinary water and rinse your ladle before putting it back on the rim of the basin. I find this process is a way to express the desire to get closer to the world of Buddha. It is 'only' symbolic, but symbols are important. You may want to dry your hands and mouth with a handkerchief.
The next thing I do is check the incense situation. Large temples usually have a large incense burner in front of the main hall and in front of other important structures or statues, so you can check to see if there is a place to buy a bundle of incense. At Sensoji, you can get a bundle of incense for ¥100. There are hibachis with super-hot charcoal that will get your incense fired up. This is especially fun on a hot day! (Just kidding, but in winter, the heat is welcome!) Check to see that your bundle is completely ignited. If it is flaming, do not blow out the flames--it is better to wave you hand at the bundle to extinguish the flames. Then, being careful not to run into anyone, carry your bundle to the incense burner and place it upright in the ash bed. This can also be quite hot, so I try to do it as quickly and gracefully as possible. Then, face the main hall to acknowledge the Buddha inside. Some people will hold the incense in a gesture of offering before placing it in the burner--this is done more elaborately in other Asian countries, not so much in Japan. Visitors to Japanese temples like to believe that the smoke from the incense burner is good for them--they may pat the smoke onto a sore shoulder, or onto the head to hope for better performance on a school examination or something like that. This is one of those 'folk' traditions that are not really part of the doctrine, but there is little objection if people like to do that.
I haven't even gotten to the main part of the visit yet! But these preliminary procedures will make your temple visit more than just looking around as a sightseer. Some temples, like Sensoji, have lots of sightseers, so it is not such a big deal. But at a temple off the beaten path, it would be nice, and makes the locals feel a lot better, if you could add as much respectful behavior as possible.
My pix show the large incense caldron giving off a lot of smoke at the temple Zenkoji. Next, a water basin with a spout shaped like a dragon. The dragon is known as a supporter of Buddhism, and associated with Kannon/Kuan Yin. And another photo of single incense sticks in front of the main hall at Kenchoji in Kamakura.