～てみる

In order to express that you will (or someone else should) try something, the conjunction particle て will be paired with 見(み)る (almost always without kanji). While this is translated as 'to try to (A)', the actual meaning is closer to 'to do (A), and see (whether the result is good or not)'.
This grammar construction is usually only used when someone tries something for the first time.

• 本当(ほんとう)においしいの？今度(こんど)食(た)べてみるよ！
  Is it really delicious? Next time I'll try it!
• これ飲(の)んでみる？
  Do you want to try this drink?

As mentioned above, this phrase is also used when suggesting that someone else should try something. In these situations, (A) + てみて, or more formally, (A) + てみてください will be used.

• だまされたと思(おも)って食(た)べてみてよ。
  Try and eat it as if I tricked you into eating it. (Believe it or not, this tastes good)
• もう一度(いちど)電源(でんげん)を切(き)ってみてください。
  Please try to turn it off once more.

Sometimes, in very casual situations, even the て will be dropped, and (A) + てみ will be used by itself. This usually has the nuance of 'come on, just give it a go!'

• このボール投(な)げてみ。
  Try and throw this ball.