Actually Britain was somewhat of a latecomer when it came to the colonial race.
The first 'discovery' was Newfoundland in 1497 but they didn't found any colonies for a while. During the 16th century they mainly envied along with the french and dutch the huge riches that were pouring into portugal and spain due to their newly founded colonies. The first surviving colony was Jamestown founded in 1607, followed by St. Kitts 1624, Barbados 1627, Nevis 1628. Roanoke(1585-1587), Guiana(1604), St. Lucia(1605), Grenada(1609) didn't survive.
If you compare this to Spain and Portugal... well they had it all
At the Battle of Beachy Head (1690) the French crushed the English and pretty much isolated them on their island.
The most devastating blow altough was dealt at The Battle of Lagos (1693). This defeat pretty much bankrupted England and gave France a huge money boost on the other side. If it hadn't been for a new establishment founded in 1694 'The Bank of England' there would've probrably been no British Empire to follow a hundred years later. This gave the government the money it desperately needed to completely rebuild it's fleet.
The 'Britsh Empire' as we mainly understand it today was a long struggle with many setbacks (as noted above) along they way. It mainly prevailed due the role of the Royal Navy. Which had become the most effective 'war machine' in the world during the 18th-19th century.
This dominance became undoubtably clear at the Battle of Trafalgar in 1805 which pretty much gave them sole access to the worlds oceans for about 100 years following. In which time they also annexed pretty much all the French colonies after the fall of Napoleon. Thus completely driving them out of America and India.
Following all this came 'Queen Victoria' (1837-1901)(Empress of India 1876-1901) also known as the 'Victorian Age' in which Britain had it all..
But that would be after the time-period of the mod.
Spanish example:
The Laws of the Indies had the Laws of Burgos, 1512-1513, the first codified set of laws governing the behavior of Spanish settlers in the Americas, particularly with regards to native Indians. They forbade the maltreatment of natives, and endorsed the Indian Reductions with attempts of conversion to Catholicism. Upon their failure they were replaced by the New Laws (1542)
One of the most accomplished conquistadors was Hernán Cortés, who leading a relatively small Spanish force but with local translators and the crucial support of around two hundred thousand Amerindian allies, won Spanish conquest of the Aztec Empire in the campaigns of 1519–21, becoming the Spanish empire's colony named the Viceroyalty of New Spain, present day Mexico. Of equal importance was the Spanish conquest of the Inca Empire by Francisco Pizarro, which would become the Viceroyalty of Peru. After the conquest of Mexico, rumours of golden cities (Quivira and Cíbola in North America, El Dorado in South America) caused several more expeditions to be sent out, but many of those returned without having found their goal, or having found it, finding it much less valuable than was hoped. Indeed, the New World colonies only began to yield a substantial part of the crown's revenues with the establishment of mines such as that of Potosí (1546). By the late 16th century silver from the Americas accounted for one-fifth of Spain's total budget.
In the 16th century "perhaps 240,000 Europeans" entered American ports.
Portuguese example:
The squadron of Vasco da Gama left Portugal in 1497, rounded the Cape and continued along the coast of East Africa, where a local pilot was brought on board who guided them across the Indian Ocean, reaching Calicut in western India in May 1498. The second voyage to India was dispatched in 1500 under Pedro Álvares Cabral. While following the same south-westerly route as da Gama across the Atlantic Ocean, Cabral made landfall on the Brazilian coast. This was probably an accidental discovery, but it has been speculated that the Portuguese secretly knew of Brazil's existence and that it lay on their side of the Tordesillas line. Cabral recommended to the Portuguese King that the land be settled, and two follow up voyages were sent in 1501 and 1503. The land was found to be abundant in pau-brasil, or brazilwood, from which it later inherited its name, but the failure to find gold or silver meant that for the time being Portuguese efforts were concentrated on India.
Profiting from the rivalry between the Maharaja of Kochi and the Zamorin of Calicut, the Portuguese were well received and seen as allies, getting a permit to build a fort (Fort Manuel) and a trading post that were the first European settlement in India. In 1505 King Manuel I of Portugal appointed Francisco de Almeida first Viceroy of Portuguese India, establishing the Portuguese government in the east. That year the Portuguese conquered Kannur where they founded St. Angelo Fort. Lourenço de Almeida arrived in Ceylon (modern Sri Lanka), where he discovered the source of cinnamon.
But in any case this is all totally beides the point and would be more fitting in the UHV discussion thread once it possibly comes up
There's a quite nice 4 part BBC Documentary on the subject called 'Empire of the Seas'