See if this explanation does the trick:
In Delaware, it only takes one person to incorporate. So I could go to Delaware and incorporate twice, once as Talent Ltd and again as Writers Inc. They are closely-held corporations and I own all the stock. I am the President, Vice President and Secretary-Treasurer of both corporations, and I am their sole employee. Writers Inc and Talent Ltd have their own assets, their own liabilities, their own income tax returns. If you sue Writers Inc and win, it does not affect either Talent Ltd or my personal finances, as long as I don’t cosign any loans. That’s why people incorporate their businesses: it makes the business a separate legal person so that business losses don’t affect personal holdings.
Now we have three legal persons: Ken Collins, Talent Ltd, and Writers Inc. Talent Ltd markets writing services to clients, Writers Inc supplies the services, and sends me to do the work. I have to ask Talent Ltd for my paycheck, Writers Inc bills Talent Ltd for the money, Talent Ltd bills the client.
There are three persons, but I am one human being; in the same way, God is three persons but one God.
Talent Ltd is me. Writers Inc is me. Ken Collins is me. But that adds up to only one me. In the same way, Jesus is God, His Father is God, the Holy Spirit is God, but that adds up to only one God. Jesus is Lord, His Father is Lord, the Holy Spirit is Lord, but that adds up to only one Lord.
Talent Ltd is not Ken Collins, Writers Inc is not Talent Ltd, and Writers Inc is not Ken Collins; they are distinct legal entities, with separate liabilities and assets, but they are all one human being with the same objectives, policies, and standards. In the same way, the Father is not the Son, the Son is not the Holy Spirit, the Holy Spirit is not the Father, they have different roles, but they are all one God, with one substance, one essence, and one will.
If you say,
Show me Talent Ltd, as the disciples asked Jesus to show them the Father, I can reply,
If you’ve seen me, you’ve seen Talent Ltd.
When I am on site with a client, I can explain,
I can only do what is in Writers Inc’s corporate policy, just as Jesus said He could only do His Father’s will.
Writers Inc can issue me a business card that says
This is our trusted employee, just as the Father sent a dove and said about Jesus,
This is my beloved Son.
If Talent Ltd closes its branch office in a town, a client may say,
Please don’t leave. And I might reply,
Talent Ltd is leaving town, but Writers Inc will handle the business. I am staying with you. In the same way, Jesus could leave the disciples, yet be with them always by sending the Holy Spirit.
Of course there are flaws in this limited analogy. First, in my example, Ken Collins is a natural person, while Writers Inc and Talent Ltd are only legal persons. All three persons of the Trinity have the same status. In my example, I had to go to Delaware and incorporate. But God did not need to go to Delaware and never started being the Trinity. Nevertheless, it shows that the Trinity is not really hard to understand.
You can read the Athanasian Creed for more authoritative information about the Trinity.