Darrell C, this post is rather long but if you really would read it in it's entirety you will see what is the Catholic way of praying to Mary and the other saints in heaven.
		
		
	 
Long? I am writing the book on long posts (still writing it which is why it is so long, lol).
As with all denominations there is a range within the Doctrine of each individual that usually runs from nominal to fanatical. The following statements can be seen, I think, to be a rational and understandable explanation of your view concerning a Catholic position on praying to Mary and the (passed away)saints. However, having spoken with many claiming to be Catholic I have come to find that while some have a very conservative view of certain doctrine of dispute among the denominations, some have stepped into a fanatical and (understandably) heretical doctrine which does in fact worship Mary and reaches out to her just as we would in our supplications to God, Who alone has the power to answer prayer.
Encounters with such leads to a tendency on the part of those opposed to such doctrinal views for hostility, and while I know there are many well meaning and sincere Catholics who love God and seek to do His will, there remains an obligation to clarify between what a particular denomination teaches and how that translates to the individual's personal understanding and practice of that particular branch.
The breach between Catholics and other groups (whether they be Protestant or not) remains and will likely always remain until such a time when the more fanatical branches depart from what is viewed as contrary to Scripture and those who take a more conservative view become more active in discussion with opposing groups. Personally, I am not one who writes off the entire Catholic Church based on several doctrinal positions I take issue with, but, I understand that just as with every group, not everyone claiming to be representative of that group actually represent the Doctrine of said group.
In regards to the issue of praying to saints and Mary, I will assume you have a more conservative view, as expressed in this post. I have spoken with those who call Mary the 
Co-Redemptrix, which is of course contrary to Scripture and the basic premise of salvation in Christ Jesus. Because the tradition of praying to Mary (specifically, praying to saints aside) implies more than a veneration of Mary (which I think is proper, given her role as the physical mother of Messiah) and unless carefully explained can lead to confusion which leads to hostility.
	
		
	
	
		
		
			“Pray” for non-Catholics is synonymous with worship. But, not all prayer is worship. There are four types of prayer: 1) Worship 2) Thanksgiving 3) Petition and 4) Intercession.
		
		
	 
I can appreciate the explanation, yet I would suggest that prayer should always, from my view, be directed to the Lord. I do not ignore that prayer might be categorized, but for the sake of the focal point let's keep it simple: in view is Who we petition, and while we do, among the living, seek the prayers of others, when we do, their prayers also will be directed specifically to the Lord.
You might want to add imprecatory prayer to your list, by the way.
	
		
	
	
		
		
			The original meaning and use of the word “Pray” is to “petition” or “ask.” The practice of petitioning Saints or Mary dates to the earliest days of Christianity and is shared by Catholics, Eastern Orthodox, the other Eastern Christians, and even some Anglicans—meaning that all-told it is shared by more than three quarters of the Christians on earth—It has only been with the advent of Protestantism (500 years old or less) that anyone has questioned the use of this word.
		
		
	 
When we speak to those that have passed on, implied is an ability I do not see a basis for in Scripture. Again, when we petition prayer among the living, their prayers will also go to the Lord. While the living are exhorted to prayer, the result is that their relationship with God is increased, meaning, the Lord is not left out of the loop but is the very One each individual appeals to. 
In regards to conflict with prayer to Mary or Saints, while the practice may be ancient, one of the primary basics of Scripture is to exhort men not to even imply worship of any god other than God Himself. When Israel sinned in supplication to other gods, their sin was not to turn to the only One Who could actually give aid. 
	
		
	
	
		
		
			As Scripture indicates, those in heaven are aware of the prayers of those on earth. 
This can be seen, for example, in Revelation 5:8, where John depicts the saints in heaven offering our prayers to God under the form of “golden bowls full of incense, which are the prayers of the saints.”
		
		
	 
Surely you have more than this as a justification for praying to Mary and the Saints.
Revelation 5:8
King James Version (KJV)
8 And when he had taken the book, the four beasts and four and twenty elders fell down before the Lamb, having every one of them harps, and golden vials full of odours, which are the prayers of saints.
I do not see the Elders offering up the prayers of the Saints here. In fact...
Revelation 8 
King James Version (KJV)
3 And another angel came and stood at the altar, having a golden censer; and there was given unto him much incense, that he should offer it with the prayers of all saints upon the golden altar which was before the throne.
4 And the smoke of the incense, which came with the prayers of the saints, ascended up before God out of the angel's hand.
...it seems that the prayers of the Saints is offered up by this Angel. "All Saints" would, I would think, include the Saints which have been titled Elders, right? And these prayers come to God, with no distinction given as to having been maintained by the Elders, or intervention taken on the part of the Elders. 
But I would be curious as to any other Scriptural Basis for the practice.
	
		
	
	
		
		
			So, we do pray to saints, but not to worship them. We pray to ask for their prayers.
		
		
	 
I can understand that, and personally don't see it as a big deal, though I myself would not engage in it. Why do that when I can directly to God?
The Old Testament presents a basic principle that approach to God was primarily through particular servants of God, Man being separated from direct contact through sin (which is a general conclusion based on the whole of Scripture, seen in retrospect). The New Testament opens the door, or rather, tears down the veil that separated man from God and provides direct approach. Seeking another Mediator other than Christ does not make sense to me, and while it can be viewed as no different than appealing to the living for prayer, the difference would be found in the expected result of the prayer. The call for us to pray for each other implies and insists on a personal relationship with God, rather than the denied access seen in previous Covenants. I do not ask others to pray for me because I feel the Lord is for some reason not going to hear me, but because I trust in the premise that they, as I, have a relationship with God.
But I am a little different than some in my prayers, I believe I can ask the Lord once about something and were done. I don't have to keep reminding Him. 
Continued...