If you haven't learned the verb endings yet, look here. It's also important to know about subject and object. If you hover the mouse pointer over the examples below, you will see a translation.

Transitive (two-link) verbs

Definition: Verbs that can have an object.
Examples: Mi havas fraton. - Ŝi naskis filinon. - Li ludas gitaron.
Explanations:

• A transitive verb can also be called a two-link verb since it can have a link either to the subject (the person or thing performing the action) and to the object (the person or thing affected by the action).
• NB: The definition is "a verb that _can_ have an object", but that doesn't mean that it always has an object, for example:
  Mi ludos vespere. - Li manĝis.
• The suffix -iĝ- makes a transitive verb intransitive, for example:
  (Ŝi naskis filinon.) - La filino naskiĝis hieraŭ.

Intransitive (one-link) verbs

Definition: Verbs that can NOT have an object.
Examples: La arbo falas. - Mi ĝojas pri tio. - Aperis kelkaj problemoj hieraŭ.
Explanations:

• An intransitive verb can also be called a one-link verb because it has a link only to a subject (the person or thing performing the action), but not to an object.
• The suffix -ig- makes an intransitive verb transitive, for example:
  (La arbo falas.) - Mi faligas la arbon.

An additional explanation about "links"

Think about the sentence "I live in a house". Is "live" a one-link (intransitive) or two-link (transitive) verb? Because "to live" can't have an object, it must be a one-link verb. But what about "house", doesn't "live" link to "house" in the sentence "I live in a house" (in Esperanto: Mi loĝas en domo)? Not directly. When you link with a preposition (in this case, "in"), the noun linked by the preposition is not the object. Prepositions are like "links". Think about the sentence "I eat an apple in a house" (In Esperanto: "Mi manĝas en domo pomon"). In that sentence, "apple" (pomo) is the object of "eat" (manĝas), but "eat" doesn't have its own link, or any direct link to "house" (domo).
Conclusion: If the verb can have a link only by preposition (except to the subject), it is a one-link verb.

About the suffix -ig-, with relation to verbs

When you use -ig- in a verb, the verb gains one link, for example:

• La arbo falas. (unu ligo) - Mi faligas la arbon. (du ligoj)
• Li kantis novan kanton. (du ligoj) - Ŝi kantigis nin. = Ŝi igis nin kanti kanton. (tri ligoj)

About the suffix -iĝ-, with relation to verbs

When you use -iĝ- in a verb, the verb has one link less than it otherwise would, for example:

• Mi renkontis novan amikon. (du ligoj) - Ni renkontiĝis hieraŭ. (unu ligo)
• Min interesas libroj. (du ligoj) - Mi interesiĝas pri libroj. (unu ligo)

Note: The explanations below are primarily for students who are perfecting their knowledge. Don't worry if you don't understand it very well.

About participles relating to -ig-, -iĝ-, and verbs

The passive participles (-it-, -at-, -ot-) can't be used with an intransitive (one-link) verb, because they only express a quality of the thing that is affected by the action (and with an intransitive verb, you have only the thing performing an action - nothing is acted on). For example, it's not possible to say "La akvo estas bolita" (The water is becomes boiled), you must say "La akvo estas boligita" (The water is having been boiled)