Learn French: Je tiens mon billet. - I am holding my ticket.

Tiens is the "I" form of the verb tenir (to hold). It is included here because tenir follows the exact same irregular conjugation pattern as venir. Just as "I come" is je viens, "I hold" is je tiens. Once you learn the pattern for venir, you automatically know how to conjugate tenir!

Why doesn't the French sentence have a word for "am" like the English translation "I am holding"?

French doesn't have a direct equivalent to the English "-ing" tense (present continuous). The single French present tense covers both meanings! So, je tiens translates to both "I hold" and "I am holding" depending on what makes sense in the context.

Why is it mon billet instead of ma billet?

In French, possessive words like "my" (mon, ma, mes) must match the gender of the object being owned, not the gender of the owner. Because billet (ticket) is a masculine noun, you must use the masculine mon, regardless of whether the person holding the ticket is a man or a woman.

Do I pronounce the final 's' in tiens or the final 't' in billet?

No, both are silent. As a general rule in French, consonants at the very end of a word are not pronounced unless they link to a vowel in the next word.