Languages that use Latin alphabet (English included) mark proper nouns using capitalization, but this convention is not something found in every language. See Alternative marking of proper names. The Japanese orthography does not have a way to explicitly mark proper nouns, either. In most cases, however, marking proper nouns is not necessary; a fluent speaker can usually tell whether a word is a proper noun without any markers, just as you can do so in speech.
That said, while English has only two types of alphabet (uppercase and lowercase), Japanese has at least three (kanji, katakana and hiragana), and their distinction is very important. In a broad sense, we take advantage of these three "alphabets" to distinguish many contexts. This distinction is also what allows us to read and write sentences smoothly without any spaces. In modern standard Japanese, hiragana are primarily used to write function words (particles) and show inflections, katakana are primarily for foreign words and onomatopoeias, and kanji are primarily for most common nouns and verbs. See Japanese writing system for details.
So we can distinguish some pairs like so:
- the joker = その野郎 (as a common noun meaning guy or fellow)
- The Joker = ジョーカー (as a foreign proper noun)
- queen Mary = メリー女王 (as a queen, a common noun, whose name is Mary)
- Queen Mary = クイーン・メリー (as a foreign two-word proper noun)
Unfortunately, there is no easy way to distinguish the internet (generic internetwork) and the Internet (WWW) since both are recent loanwords; both are rendered as a katakana word インターネット. In such rare cases, imagine how you distinguish them in speech in English. You can simply pick a different word (e.g., the Web), but occasionally you may end up saying something like "This is a proper noun".