Clouds of the west! sun there half an hour high! I see you also face to face. (line 2)
The poem begins a half an hour before sunset. If you follow the imagery of light and shadow, you'll notice that the poem seems to grow darker as it goes along.
And you that shall cross from shore to shore years hence, are more to me, and more in my meditations, than you might suppose. (line 5)
The speaker isn't one to "live for the moment," as they say. Or maybe he is living for the moment – two hundred years from now. He thinks a lot about the future, and about what kind of people will be making the same crossing as he.
Fifty years hence, others will see them as they cross, the sun half an hour high, A hundred years hence, or ever so many hundred years hence, others will see them, Will enjoy the sunset, the pouring in of the flood- tide, the falling back to the sea of the ebb-tide. (lines 17-19)
Continuity is a big concern in this poem. It gives the speaker comfort to know that things will proceed more or less in the same way for all time. Same sunset, same tides, same angry commuters trying to get home after a long day at the foundry. Okay, maybe not the last one.
It avails not, neither time or place – instance avails not, I am with you, you men and women of a generation, or ever so many generations hence, I project myself – also I return – I am with you, and know how it is. (lines 20-22)
The speaker sends himself into the future on a mission: to make friends with us and empathize with all our little problems. For him, time doesn't "avail," that is, it doesn't succeed in putting up obstacles between people.
Others the same – others who look back on me, because I looked forward to them, (The time will come, though I stop here to-day and to-night.) (lines 55-56)
He explains more about how this connection to the future works. From the reader's perspective, our "looking back" on Whitman is what makes it seem like he is "looking forward" by speaking to us. But he's like, "No, no, I was the one who made the first move." Also, he makes it sounds like he exists in the present only by choice, because he chooses to "stop here to-day and to-night."
What is it, then, between us? What is the count of the scores or hundreds of years between us? (lines 57-58)
The implied answer to these rhetorical questions is: nothing. What's a couple hundred years between old friends who've never met each other?
You have waited, you always wait, you dumb, beautiful ministers! you novices! We receive you with free sense at last, and are insatiate henceforward, (lines 141-142)
The things of the world were always there in the same form: they were just waiting for somebody like Whitman to come and "discover them." From now on, he says, we're won't be able to live without them. We'll be "insatiate," meaning we'll always be hungry for more and more things of the world. Past, present, and future come together in these lines.