As far as I know, one can say "I started doing X" by adding X-はじめました。 However,
I don't think this applies to "to like", which is an adjective. So how to say
for example "I started liking science"
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2014-05-11T16:18:45.760
15879
2014-05-13T06:20:28.713
2014-05-13T06:20:28.713
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question
grammar adjectives
How to say "To start liking something"
It would literally be:

> [科学]{かがく}が好きになり[始]{はじ}めました。  
>

...using the verb なる(成る;grow/become) and 始める. But I think you could also say
it as:

> 科学が好きになってきました。  
>

...using なる and the subsidiary verb くる(来る).
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2014-05-11T16:26:14.743
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2014-05-11T16:44:29.227
2014-05-11T16:44:29.227
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answer
I think that 好きになった, as in [Chocolate's
answer](https://japanese.stackexchange.com/a/15880/1628) is the best literal
way of saying "I started liking...".

Another very common way of expressing the same sentiment is to use 気に入{い}る.
Often translated as "favourite X" in the expression お気に入りのX, when used in the
verb form 気に入った it aptly describes that you started liking something, the past
tense here pointing at the transition to the "state of liking". So,

> I started liking science.  
>  科学が気に入った。
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2014-05-11T21:35:53.997
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2014-05-11T22:26:37.123
2017-04-13T12:43:44.863
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answer