I can't give as detailed an account as others but I know the gist.

At the beginning of the spice wars (as this period of colonialism is called) Venice was the dominant trader in foreign spices. Their routes being long and traveling through Muslim countries made spices expensive for Europeans. Eventually (due to other factors as well) Portugal sends some expeditions around Africa to bypass the Muslims and Venetians. After a couple unsuccessful trips one expedition returns with more spices than Venice brought in in a year. All of a sudden Lisbon is a trade hot spot and Portugal goes from backwater mid power to an integral spot of European interest. Other countries send out expeditions in search of the riches Portugal found. Primarily Spain.

Now Spain was the player in Europe. I believe they held the crown of the HRE at this point and their navy was too tier shit (they also owned the Dutch lowlands which is important to remember). So this is a big factor to why an Alliance developed between the seafaring England and Portugal.

This is where the Anglo-Portuguese alliance begins to fall apart.

A number of things all of a sudden go right for England. The Spanish Armada is crippled from a hurricane the Dutch revolt and form Holland (with some English bank) and Columbus finds the Caribbean. This leads to a weakened Spain whose focus is on Central and South America more than the Indies (which becomes the focus of Portugal, England and Holland).

Now as Portugal was the first to the Indies they are the first to have relations with the powers in the area and the first it have colonies which makes them the target of the entrants to this market: England and Holland. As well, now that Spain has been nocked down a few pegs the Anglo-Portuguese alliance is not as necessary.

So the English do what anybody would do in this situation. Ditch the Portuguese alliance for one with the Dutch (whom they formed a decent bond with during their revolution from Spain). The English and Dutch tag team the Portuguese through pirates in the Indies and closer to home to disrupt their economic gains.

From here Portugal and Spain become closer (for a short time are unified under the same monarch) and after their bit with the Portuguese the English and Dutch turn on each other.

This of course happens over a span of about 200 years cause sailing.

Hope this helps a bit at least. I might have left out some details, like I said I know the gist I'm no expert.

You can mostly ignore SincerePacifist's answer. He just takes random events from that period in history and connects them in ways that don't make sense.

Let's take this by steps:

1. spices from India came via Venice that bought them from the muslims from India. They were crazy expensive and every other nation in Europe wanted an alternative to get them.

2. Spain was also interested in getting an overseas empire. To avoid wars, the Pope mediated the Treaty of Tordesillas that divided the world between Portugal and Spain http://www.socialstudiesforkids.com/graphics/treatyoftordesillasmap.jpg It was mostly fullfilled until much latter, when Portugal decided to ignore it in order to amplify Brazil.

3. Portugal decided to try to go around Africa and get to India. They succeded and became the major world power for a while, spreading from current Iemen to Japan and Indonesia.

4. Two of the main clients of Portugal were the English and the Dutch. As long as they could buy the spices, they didn't have much interest (or hability) to go get them themselfes.

5. The king of Portugal dies in battle in Africa. He's succeded by his uncle, an old cardinal that couldn't have kids. 3 options appear to the throne. The most powerfull one gets it: Philip II of Spain. Portugal and Spain have the same king for 60 years.

6. While Portugal was friends with England and Dutchland, they were enemies of Spain. So, the king orders the portuguese to stop making deals with them and uses the portuguese army to attack England (a lot of the portuguese Navy was part of and destroyed with the Spanish Armada).

7. The English and the Dutch decide to go get the spices by themselfes. While doing that they steal a lot of the Portuguese Empire in the East, that wasn't being very well taken care of my the Spanish king (and also chuncks of Brazil that were latter recovered).

8. The portuguese revolt after 60 years, a new King is put in place and request the help of the english to keep the spanish away. The english prefer to ally themselfes with the portuguese instead of the dutch and the old status quo is instated (altough former portuguese territory is not given back). Portugal gives Bombaim and Tangier to the english. Relations with the Dutch continue to be quite bad as they were still aiming for portuguese territory.

9. By this time, both the English and the Dutch had big empires and weren't respecting the Treaty of Tordesillas. Interests from the Portuguese and English empire rarely were incompatible, so not much happened. There were 2 expections:

a) independent pirates (that were actually sponsored by the english) kept pillaging portuguese ships. Small stuff.

b) a long time latter, in the Scramble for Africa, Portugal had claims over land between Angola and Mozambique. The UK wanted that land and made an Ultimatum, broking the Treaty. Portugal wasn't able to go to war with the UK around that time, so they gave them the lands. It's the accepted main reason for the Regicide that happened a few years latter and the end of the Monarchy in Portugal.

This was a big post. I'll re-read it tomorrow and fix any incoherences.