First, anyone who tells you they know what agents want or they can get you an agent if you just buy something or follow their method is being kind of jerky.
Someone who says, here are some ideas that have worked for me or may work for you, and they don't try to sell it to you are probably going to be helpful.
The fact is, you can read Poets & Writers cover-to-cover every month and analyze every statement on agents in it and still feel lost as you send your queries out and get rejection after rejection.
While it is good to do your homework--I am a huge proponent of doing your homework--agents often only know what their next manuscript/client looks like when they see it.
That said, there are some things you can do to improve the odds. The following assumes you are familiar with the query process and are not stopping here without having at least a few rejections under your belt.
1. Start simple.
I joke that I invented the best pickup line ever. It goes like this, "Hi, my name is James. What's your name?"
The point is start out as a polite human who is free of devices, artifice, and tricks. Be authentic and say hello, your name and why you are reaching out to them.
2. Show You Care
Put a little personal tidbit up front as to why you selected that agent or agency. Don't be afraid to give them a personal detail that creates a sense of connection and authenticity. Don't force it. Be human.
3. Get to the point
Don't gas on with all the ego crap that says how great you are. When you meet someone you like--maybe to be friends with or acrush--you hopefully don't talk a blue streak about how great you are.
Tell the person here is why I am writing you and what the manuscript is titled.
In business they call it the elevator pitch. In movie parlance they call it a logline. Some call it the fifty-thousand foot view. Whatever. The idea is you are telling and showing why your manuscript is compelling and a great read.
Clearly and concisely summarize the most compelling aspect of your manuscript. Though this will only be a few lines, they are important lines and worth taking your time with. This is the honey to the bear, or at least it should be.
One suggestion is to go look at movie loglines to see how they try to develop interest in just a couple sentences, but do not write a logline.
Any good introduction gives the other person a sense of want, whether it is to be friends with you or to read your manuscript. The synopsis builds the want and when it is followed by one or two tight paragraphs that really show your chops, you will increase that want.
Basically, the synopsis shows them you have a great story and the tease shows them you are a good, competent writer.
Every good query or book proposal answers two massively important questions. One, is it a compelling story well-told? Two, will it sell?
You need a very brief, affirmative, declaratory sentence or two answering the second question. The synopsis helps answer the first, but this shows them you take the business side of writing seriously.
Don't put your whole platform here, save it for the proposal, but do say if you have a very popular blog, famous people have agreed to endorse the book, you already have interest from a publisher, or whatever you can to demonstrate some business savvy.
7. Don't sell past the close
Give them a website to go to or maybe a place where you've published something, but other than that, tell them if the manuscript is complete, edited and if you have a full book proposal. Thank them for their time without trying to push them to respond or include some jokey thing as one last hail Mary.
Then say goodbye. Make sure you include your contact info and website beneath your name.
8. The Rules
There are no rules. Even the stuff above can be ignored and whatever you do work.
However, there are rules: Be authentic, be confident not an egomaniac, be polite, try to make friends not dominate, show why your manuscript is great, and answer the two big questions.
This is why most advice for agents is repetitive or over the top in the promises made. A lot of what you do is done by gut feel. There is no magical formula for success.