がある is a common construction that is simply a combination of the が particle, and the う-Verb, ある. This expression means ‘to exist’, or ‘there is’, and is used in relation to non-living/inanimate things.

• 明日（あした）、テストがある。
  There is a test tomorrow.
• 部屋（へや）に椅子（いす）がある。
  I have a chair in my room.

Because the things being described in these examples are not considered to be ‘alive’, ある is the verb that will be used. いる is used for living things.
The polite form of ある conjugates as あります. Due to the る changing to り, we can determine that ある is a う-Verb (Godan verb). However, ある is irregular in that the plain negative form is ない, not あらない.

• キッチンにケーキがある。
  There is a cake in the kitchen. (Correct example)
• キッチンにケーキがあります。
  There is a cake in the kitchen. (Correct example)
• お金（かね）がない。
  I have no money. (Correct example)
• トイレがありません。
  There is no toilet. (Correct example)
• にんじんがあらない。
  Theren’t carrots. (Incorrect example, with incorrect English to match!)

The kanji form of 有（あ）る is quite common, and should be learned as early as possible, to save any confusion while reading. There is no nuance difference between this expression being used with, or without kanji, and is up to the preference of the writer.

• 今日（きょう）は時間（じかん）が有（あ）る。
  I have time today.