I’m based in London, but I live in New York. 
This phrase is used when you want to make it clear that your current living situation is temporary, or you do a lot of traveling because of your job.

I live in New York, but I’m originally from Lisbon. 
English speakers like to use this phrase when mentioning their native country or city. It’s more common than phrases like I was born in / I grew up in.

I’m a colleague of Jane’s. 
When introducing yourself in a group or at an event (like a party or a conference), it’s helpful to explain your connection to other people in the group or event. Similar phrases include: I work together with Jane / I’m Jane’s brother / Jane and I both study Chemistry at Toronto University.

I’m the father of two young girls. You can use this phrase if you want to say something about your family (it’s also a simple way for parents to explain why they don’t have much “free” time). Similar phrases include: I’m the daughter of two psychologists / I’m one of eight children / I’m the son of Queen Elizabeth.

These phrases are good for both formal situations like job interviews, as well as casual situations like parties.
I work at English Experts in the Marketing Department. When English speakers want keep their introduction simple (and avoid giving long or complex titles like Senior Vice President and General Manager of North American Sales for Behemoth Enterprises), they often just give the name of the company, and perhaps their department. This phrase also works for students: I study Chemistry at Toronto University / I’m a student at Toronto University, in the Chemistry Department.

I have worked at English Experts since 2012 / for 8 years. Details about time are nice to include in your self-introduction, but remember that English requires a different verb tense (known as the present perfect) when you use the prepositions for or since.
I’m responsible for managing the digital marketing campaigns. When introducing yourself to people in the same company or department, you can use this phrase to describe the most important thing you do. Similar phrases include I’m in charge of and I deal with. Notice the ing. This phrase requires a noun (or a gerund, which the noun form of a verb), so you can also use nouns with these phrases: I’m in charge of the website / I deal with the suppliers.

I hold a master’s degree in Chemistry from Toronto University. This phrase is useful when you want to highlight your educational achievements, but it is typically only found in cover letters and formal documents. In conversation, English speakers use a slightly more informal phrase: I have a master’s in Chemistry / I have an M.A. in Chemistry.

When not in the office, you can find me on the football pitch. This is a nice alternative phrase for mentioning other activities, especially if you have many sentences that start with I (I work… I’m responsible… I hold…). When not studying Chemistry, you can find me spending time with my family. Notice the ing endings.