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Great questions! A lot of the nuts and bolts of starting up a colony aren't well documented by participants, but there's a lot we can learn from their own accounts, and from subsequent secondary studies. For this answer, I'm going to assume that your target destination is the North American continent, proper - somewhere like Virginia or thereabouts - and not a Caribbean island.

Before you set sail

Colonies weren't, as they are sometimes represented popularly, exploratory endeavors, they were businesses. They were companies, formed on the basis of establishing a profitable colony, with a duty to their investors, who bought or were otherwise awarded a charter. The charter would largely have determined where you were to establish a colony, and the leadership structure of it. Within those bounds, colonial leaders were given a fairly free hand to select the specific area of their colony, and were able to pursue lucrative trade commodities as they found them.

You would also need to hire ships, and bring along laborers. The majority of early colonists were indentured servants, contracted for a specific amount of time, to be remunerated with a parcel of land in the new colony when their contract was fulfilled. I go into more detail on this in this post

But, once all your ducks were in a row, you were ready to begin your voyage.

When you sight land

Sighting land is the easy part, and will probably happen several times before you even sight the proper continent of North America. Because of sea currents and wind, the most likely route you'd use to get to where you're going would bring you south, to the coast of Africa, and then west, either to the coast of South America or one of many islands in the Caribbean. John Smith records that, in the voyage to Virginia to found Jamestown:

after many crosses in the downes by tempests, wee arrived safely uppon the Southwest part of the great Canaries: within four or five daies after we set sail for Dominica

Later, they arrived at

the verie mouth of the Bay of Chissapiacke, which at that present we little expected, having by a cruell storme bene put to the Northward

Making landfall

Some colonies knew where they were going more exactly, but the early efforts often had to try to find hospitable areas which could support the colony in its vulnerable early months. At issue here is less "hostile native attack" and more "we need shelter, food and places to store it, fuel for hearths, and fresh water." Also necessary was a stockade or palisade wall, and some form of military organization against possible attack, not only from hostile native groups (a very real possibility, as we'll see in a moment), but also from forces from competing nations' colonies, as well.

The Jamestown colony is somewhat infamous for its terrible location. They were next to swampy, dirty water, in an area uninhabited by the local Paspahegh because it was unsuitable for agriculture. Ideally, what you’d want is a location free of too many locals, on arable land suited for agriculture, not too far from commodity resources and building materials, and very close to fresh water, and access to the sea. Your sustenance will, for a great while, be completely dependent on resupply, so navigable water leading to and from the sea is non-negotiable.

Once the location was chosen, Smith relates what was likely a common ritual:

in that place was the Box opened, wherin the Counsell for Virginia was nominated: and arriving at the place where wee are now seated, the Counsell was sworne, the President elected... where was made choice for our scituation a verie fit place for the erecting of a great cittie

This was likely a formality, as the chief officers of the colony would have been heavily involved in the preparation of leadership before and during the voyage. In any case, this was done on the site of the future colony, and marked the official establishment of the colony.

The first night

Once the rituals of selection of place and election of officers was completed, the first night would likely be spent onboard ship.

George Percy, another early colonist, recorded the first night at Jamestown:

At night, when we were going aboard, there came the Savages creeping upon all fours, from the Hills, like Bears, with their Bows in their mouths, [who] charged us very desperately in the faces, hurt Captain Gabriel Archer in both his hands, and a sailor in two places of the body very dangerous. After they had spent their Arrows, and felt the sharpness of our shot, they retired into the Woods with a great noise, and so left us.

Smith gives another account:

twentie or thirtie went a shore with the Captain, and in coming aboard, they were assalted with certaine Indians, which charged them within Pistoll shot: in which conflict, Captaine Archer and Mathew Morton were shot: whereupon, Captaine Newport seconding them, made a shot at them, which the Indians little respected, but having spent their arrowes retyred without harme