The Old Testament is full of references that speak to the Trinity....some obvious, some a little more subtle.
Genesis 1:1- The word God chose to identify Himself here is Elohim, which is indeed a word that denotes plurality.
Later, in Genesis 1:26 God says, "Let US make man in OUR image, after OUR likeness..."
This was no coincidence.
Genesis 1:2 states "And the Spirit of God moved upon the face of the waters."
So far, in Genesis 1:1-2 we've had two of the three persons of the Godhead mentioned, each distinct from the other.
A figure referred to in several places in the Old Testament as 'The Angel of the Lord, The Angel of Jehovah, The Angel of His Prescence, etc.' (by the way, THE Angel of the Lord needs to be carefully distinguished in scripture from an angel of the Lord, another subject for a different day) is seen carrying out duties and actions clearly associated with and belonging to Jesus Christ. In the light of numerous New Testament passages, it can be properly observed that The Angel of the Lord is the pre-incarnate spirit of the Person of Christ.
The OT is ever presenting the existence of the Person of Christ and paved the way for the manifestation of Jesus in the NT.
One powerful example from Exodus 12, the last of the plagues to fall upon Egypt was the death of the firstborn in every house in the land. God told the Israelites to offer a spot free, perfect lamb and paint the blood of the sacrifice upon the door post so that the Angel of the Lord would pass over that house and they would not be subject to judgement by the Lord.
This is a wonderful and beautiful foreshadowing symbol of Jesus being the 'spot-free sacrificial Lamb of God that would keep one from death (spirtual) and judgement.
There are a multitude of other examples in the OT that point to the idea of a three-in-one Godhead.
Probably the most clear on the subject to explain it to someone who asks is found in the NT.
John 1:1 Says "In the beginning was the Word, and the Word was with God, and the Word was God." The Word is the Son and is seen here existing with God, as God from the foundations of time, the same is true of the Spirit, of which is confirmed in Genesis 1:2.
Later in verse 14 of that same passage, "And the Word was made flesh and dwelt among us...." Bringing in the third person, the Person of Christ.
Also, linking that with 1 John 5:7, where it says, "For there are three that bear record in Heaven; the Father, the Word and the Holy Ghost: and these three are one." We have a complete picture of the three-in-one Godhead.
When Jesus was baptized by John in Matthew 3, the Spirit is seen descending on Jesus 'like a dove' and at the same moment, the Father's voice is heard in Heaven saying, "This is my beloved Son, in whom I am well pleased." And for the first time, the trinity that was foreshadowed on numerous occasions is plainly manifested.
Jesus Himself asserted His Deity many times in the NT, in John 10 to list but one area.
That's how I would initially present the concept of the Trinity to someone who was wondering.