How do Catholics speak with their Guardian angels? According to Catholic teachings, how are Catholics to speak with their guardian angels?  With their voice?  In their minds?  Does the Church provide any guidance or description?
Interaction with a guardian angel will vary from person to person because it takes on the character of a spiritual encounter.  There is some guidance in the Catechism that may help answer your question.  

TL:DR; The most likely way to speak with your guardian angel is through prayer.   With the mind? Yes.  With the voice?  Yes.  In other ways?  Yes.

I'll explain how I arrive at that conclusion.  (Prayer need not be formal.  It can be informal communication of a prayerful nature). 

On the nature of Angels

In (CCC 329) St Augustine is called upon to provide insight: 


  'Angel' is the name of their office, not of their nature. If you seek
  the name of their nature, it is 'spirit'; if you seek the name of
  their office, it is 'angel': from what they are, 'spirit', from what
  they do, 'angel.'"  


In the same article, the angels' role, to include some helpful guidance from Jesus:  


  With their whole beings the angels are servants and messengers of God.
  Because they "always behold the face of my Father who is in heaven"
  they are the "mighty ones who do his word, hearkening to the voice of
  his word". (Matthew 18:10; Psalm 103)   


A few articles down, we find this heading ...

The angels in the Life of the Church

CCC 334-336 explains it with reasonable brevity.  


  ... the whole life of the Church benefits from the mysterious and
  powerful help of angels.  In her liturgy, the Church joins with the
  angels to adore the thrice-holy God.  She invokes their assistance (in
  the Roman Canon's Supplices te rogamus . . .{"Almighty God, we pray
  that your angel..."}; in the funeral liturgy's In Paradisum deducant
  te angeli. . .{"May the angels lead you into Paradise. . ."}). 
  Moreover, in the "Cherubic Hymn" of the Byzantine Liturgy, she
  celebrates the memory of certain angels more particularly (St.
  Michael, St. Gabriel, St. Raphael, and the guardian angels).  From
  infancy to death human life is surrounded by their watchful care and
  intercession.1 "Beside each believer stands an angel as
  protector and shepherd leading him to life."2


How to communicate


Collectively, the church communicates with the angels through prayer.  
Personally, any of the faithful can communicate to angels in prayer.  A classic example is this prayer to St Michael.  


  St. Michael the Archangel,  defend us in battle.  Be our defense
  against the wickedness and snares of the Devil.  May God rebuke him,
  we humbly pray,   and do thou, O Prince of the heavenly hosts, by the
  power of God, thrust into hell Satan, and all the evil spirits, who
  prowl about the world seeking the ruin of souls. Amen.   

Through our actions.  The church believes that the guardian angel stands "beside each believer" -- the implication is that the angel is aware of what the believer they have the care of is doing.  Not too far of a reach, if you already accept as a matter of faith that there are angels, and that we each have a guardian angel. 
Through personal prayer.  If the Church can collectively communicate with the angel through prayer, a single member of the faithful can do the same.  Since a guardian angel of the same nature as any other angel, prayer will work.   
Through conversation.  Be it silent and mental, or verbal/spoken communication, a key to believing that we can communicate with our guardian angel is linked to their aforementioned capacity for intercession.  Prayers for intercession are very common forms of prayer.  Given that the angel is near by, simple prayer, or a simple request prayerful or otherwise, should be effective.  


Isn't communication a two way street?

Yes.  How to listen, how to learn to listen, and how to pick up cues of response to prayer (be it angelic response or from higher authority) is one of the places where spiritual experience will vary.  You may hear your angel's voice.  I may only be provided signs and portents.  Another person may see something in particular.       

Follow up on St Augustine: since the nature of the angel is of spirit, encounters with angels take on a spiritual character.  A common form of spiritual encounter is through prayer, although there are other forms.    

What is prayer?  From CCC 2558:


  For me, prayer is a surge of the heart;
  it is a simple look turned toward heaven,
  it is a cry of recognition and of love,
  embracing both trial and joy.
  ~ St. Therese of Lisieux, Manuscrits autobiographiques   


To sum up all of the above

The most likely way to communicate with one's guardian angel is through prayer.  It isn't the only way, but based on the church's teaching on guardian angels and angels in general, it seems to simplest way to do it.  To a certain extent it probably doesn't matter, since the guardian angel is aware of what we do and what we need.  

If the desire to communicate arises  ...  communicate. 



1 Matthew 18:10; ⇒ Luke 16:22; ⇒ Psalms 34:7; 1:10-13; ⇒ Job 33:23-24; ⇒ Zecharaiah 1:12
2 St. Basil, Eunomium III, I: PG 29, 656B.