to start a company or organization that will continue for a long time

The brewery was established in 1822. 这家啤酒厂建于1822年。

These methods of working were established in the last century. 这些工作方法是上个世纪开始采用的。

to start having a relationship with, or communicating with another person, company, country, or organization

There is a strong need to establish effective communication links between staff, parents, pupils, and external bodies. 非常有必要与员工、家长、学生以及其他各方建立有效的沟通渠道。

to cause something or someone to be accepted in or familiar with a place, position, etc.

His reputation for carelessness was established long before the latest problems arose. 在最近的一系列问题出现之前，他粗心大意的问题已经是众人皆知的了。

He's established himself as a dependable source of information. 他被认为是一个可靠的消息来源。

After three months we were well established in/at our new house/new jobs. 三个月后我们在新家安顿了下来／新的工作中站稳了脚跟。

to be in a successful position over a long period of time

He has established himself as the leading candidate in the election. 他已经确立了竞选中主要候选人的地位。

When you have established yourself and made some money, you will be in a position to marry.

I spent several years trying to establish myself as a painter.

He has established himself as one of the most successful sportsmen of the century.

It can't have been easy to establish yourselves in such a competitive market.

to discover or get proof of something

Before we take any action we must establish the facts/truth. 我们在采取行动之前必须弄清事实真相。

[ + question word ] Can you establish what time she left home/whether she has left home. 你能确定她何时离家的吗／你能否确定她已经离家了？

[ + (that) ] We have established (that) she was born in 1900. 我们已经证实，她生于1900年。