テレビアニメを見[み]るときは、部屋[へや]を明[あか]るくして近[ちか]づき過[す]ぎないようにして見[み]て下[くだ]さいね。
テレビアニメ - televi(sion) anime
見る - see/watch
とき は - when [you] (とき means "time" but it is often used grammatically like this)
部屋 - room
明るくして - adverb form of 明るい, bright
近づき過ぎない - 近い combined with すぎる makes it mean "too 近い", 過ぎない < ないmeans all together this means "not too close"
よう に して - よう then に then して, te form of suru. this is grammatical thing, but it means "do the way of [not to close and bright room]
見て - て form of 見る
て下さい - means "please do [verb]"
So altogether it means "When you watch TV anime, please watch in a bright room, and not too close."
For the sake of your Japanese learning, please don't translate into romaji-ish
Just learn to read things in kana form. You can tell where one word ends and another begins in a bunch of ways: one is the kanji, another is verb endings, etc. EDIT: and the most important way is particles of course.