The te-form has a bunch of different uses, but in the case of "verb-te verb", if the second verb is not one of a list of special verbs (of which miru (見る, to see) is one), X-te Y normally means "X and Y". For example, yorugohan o tsukutte taberu (夜ご飯を作って食べる) means "(to/I/we/you/...) make dinner and eat it": yorugohan is dinner, the "o" is a particle marking the direct object, tsukuru means to make (becomes tsukutte in the te-form) and taberu means to eat. (The first word in English is ambiguous because grammatical subjects are usually optional in Japanese, plus its verbs are not inflected for person or number.)
For a number of verbs, however, if they are in the second position, the phrase gets a special meaning. If it's miru, e.g. tsukutte miru, it means "to try to make" — or perhaps more aptly, "to try and make". If it's iku (行く, to go), it means "to go X-ing": tabete iku (where taberu (to eat) -> tabete in the te-form) is "to go to eat [something]", or perhaps: "to go and eat [something]".
Not all such special verbs correspond to English pseudocoordination though; a common one is shimau (the dictionary says "to finish / to stop", but it's uncommon in bare form), where e.g. tabete shimau means "to finish eating" or "to end up eating" / "to eat accidentally" depending on context.
The analogy between English and Japanese here is likely coincidental, but it's amusing nevertheless.