The first and most basic sentence pattern can be described as follows:
Nominative Noun (NN) + esse. NN + esse.
A noun in the nominative case is expressed followed by the appropriate form of the verb esse.
This sentence pattern is used to say that something exists, i.e. "it is" or "it exists" or "there is".
To say "It is a tree" all that is needed is to take the nominative case of Arbor and then place the correct form of esse after it, i.e. Arbor est.
When using a personal pronoun in Latin, such as "I, you, he, she, we, them", it is not necessary to state the pronoun; the correct form of esse can be used by itself. Latin is described as being a Pro-drop language because it allows the speaker to omit or drop the subject pronoun.
To say "I am" or "I exist" it is not necessary to say "ego sum". It is generally sufficient to say "sum" unless a little more emphasis is required, in which case the word "ego" is used on its own. This can be translated as "I and nobody else". The form "ego sum" would be very rarely used. In the Vulgate translation of the Bible, the translator often uses "ego sum" when Jesus is speaking and this is taken as an affirmation of his Divinity.
Here is another, very similar, sentence pattern:
NN1 NN2 + esse.
In this pattern, the verb normally (but not necessarily) goes at the end of the sentence. Noun One, in the nominative case, is considered to be equal to Noun Two, which is also in the nominative case. This differs from what would be expected in English, where the object form of words must be used after the verb per English Word Order rules.
In English one would say "I am the teacher" but the word "I" has to be changed to "me" if the word order of the sentence changed, as in "The teacher is me". However, Latin does not do this. In both cases the nominative of the noun is used and will not change: "Ego magister sum" or "Magister ego sum."
Since Latin is a Pro-drop language, this sentence pattern will often sound like the first sentence pattern, giving "Magister sum." It is understood that an unspoken "ego" has been dropped.
It should also be pointed out that when using NN1 NN2 + esse it is possible to equate any two nouns, regardless of what grammatical differences may exist between them. A male noun can be equated with a female noun. A singular noun can be equated with a plural noun. A noun with gender can be equated with a noun that does not have gender.