I don't think the Church teaches that the Saints are omniscient. Therefore my question is how are they made aware of our prayers, which are directed to them?

Our communion with the Saints is accomplished in and through Jesus Christ who is the head of the Body, the Church. All the members of Christ's body, those here on earth (the Church militant), the Saints in heaven (the Church triumphant), and those in purgatory, (the Church suffering), are members of the one Body of Christ, and are united by him, and through him who is the Head. 
 
To use an analogy, my right hand has communion with my left hand, not because my hands have their own capacity to work together. Rather, my right hand and my left hand have communion and can work together only in and through the head of my body, which unites and directs them. And so it is with the members of the Body of Christ. In this regard, St. Paul teaches, when one member suffers all the members suffer, when one member is glorified, all the members are glorified (1 Cor 12:26). And there is thus a communion of all the members in the one Body. 
 
That the Saints are aware of us, and pray for us before the throne of God is attested in Scripture where in the four living creatures present before the throne of God and where the incense, which is the prayers of God’s saints, are brought before the throne (Rev 5:8). There is also the ancient tradition of the church from apostolic times wherein the martyrs and heavenly Saints are invoked for help of every sort. 
 
Let us be clear that such communion of the Saints does not occur apart from Jesus Christ, but rather, it is facilitated by him through whom and in whom all things are and subsist, and who is the head of the Body the Church uniting his members.