The wording of the Amidah–the 19 blessings, praises, and requests at the heart of each prayer service–is precise, like a treasured family recipe that is not to be tampered with. Its text was written by our greatest sages who sensed the exact wording to be used in our prayers for every need and every season, and each word contains layers of meaning. By using this formula, we give our prayers far more power than what we can reach on our own.
But prayer is also meant to be personal. It needs to be our Amidah. This largely happens through our mind and heart. Our thoughts and feelings accompany the words or prayer and give them a flavor that is uniquely our own.
In addition, there are a few places in the Amidah where we can personalize the actual wording.
For starters, you can insert a short personal prayer within each of the middle 13 blessings of the Amidah. Such a prayer should fit the theme of that specific blessing. For example, ask for the speedy recovery of specific person within the blessing of Refa-enu (Heal us), or pray for livelihood in the blessing of Barech Aleinu (G‑d grant blessing).
Requests that are unrelated to any of these 13 blessings can be added to the blessing of Shema Koleinu (Hear our voice) since its theme is a general request for our needs. Your personal prayer should be added before the blessing's concluding words: ki attah shome'a tefilat kol peh... ("for You hear the words of every mouth...").
Another place for personal prayer is the end of the Amidah, before you recite the second Yiheyu leratzon... (May our prayer be desirous to You...).
Shulchan Aruch, Orech Chaim 119:1.