It's not a best practice to put all your email into Salesforce.
Nevertheless, if you want to automatically forward incoming emails from Gmail into Salesforce, here are instructions from Salesforce Help:
Knowledge Article Number: 000176365
I have enabled Gmail-to-Salesforce(email-to-salesforce) and I want all of my incoming email to automatically be forwarded to Salesforce.
This can be done using Gmail's Forwarding setting. The biggest hurdle to this is that the user must verify the email address that they wish to forward to, in this case the email to salesforce address. The following are the steps to do this.
1. First, you need the email address that gmail's verification email is coming from. The easiest way to do this is to go into Settings then "Forwarding and POP/IMAP" in gmail and add a new forwarding address to another email account that you have access to. Once you receive that email copy the from address, it will typically look something like mail-noreply@google.com, it might have your email domain instead of google if you have a business account.
2. Now go into Setup || Email (under personal setup) || My Email to Salesforce and add the address from step 2 to your list of "Acceptable Email Addresses" along with your normal gmail address where the email will be forwarded from, separate them with commas.
3. Also on this same page under Email Associations also change the setting to always send emails to your unresolved items temporarily, this is needed so that the verification email will show up, it can be changed back afterwards. Once that is done then click Save at the bottom.
4. Now copy the email to salesforce address at the top of the page and go into Gmail and add that as a forwarding address and send the verification email.
5. If things are set correctly you should now be able to go to your Unresolved Items and access the verification email, either copy the verification code over or click the link to finish verifying. Once that is done you should be able to enable forwarding and your incoming emails should now come into Salesforce.
See: Configure email forwarding from Gmail to Salesforce for Email-to-Case
Knowledge Article Number: 000170989
Customer want to set up a forwarding filter from their gmail account to Salesforce Using to Email to Salesforce feature. When the verification link is sent to the Email to Salesforce service email address, It bounces. The set up process is incomplete.
Add mail-noreply@google.com to "My Acceptable Email Addresses Box " on the My Email to Salesforce page. Follow this click path.
1. Click on your Name / Setup/ Email/My Email to Salesforce.
2. Paste mail-noreply@google.com in the My Acceptable Email Addresses Box
3. Then Click Save.
Then Follow the steps in setting a forwarding filter from gmail. Here is a link to the steps in Gmail support:
See: Automatically forward Gmail messages to another account
Gmail lets you automatically forward incoming mail to another address.
Here's how to forward messages automatically:
See: Configure email forwarding from Gmail to Salesforce for Email-to-Case
By forwarding incoming email into Salesforce and/or by BCC'ing outgoing email into Salesforce, you don't have the option of selecting who and what the emails should attach to in Salesforce.
That's one of the many ways Cirrus Insight adds value. It enables you to save emails to specific leads, contacts, cases, opportunities, and any standard or custom objects in your Salesforce org.
Cirrus Insight also provides you with instant Salesforce lookups in Gmail. Plus, it enables you to create leads, contacts, tasks, events, cases, and opportunities on the fly from Gmail, and it provides best-in-class calendar sync.