How do i get around the two step verification process and sign into my gmail account?

This page suggests there's an Edit link to change the phone number:

Change how you get verification codes

1. Go to your Google Account. You might need to sign in.
2. Under "Sign-in & security," select Signing in to Google.
3. Choose 2-Step Verification.
4. Under "Voice or text message," next to a phone number, select Edit .
5. At the bottom, select Change Phone.
6. Follow the steps on the screen

Using public library computers without security precautions can be hazardous to your online identity. Particularly with online services, you should enable 2-factor authentication for your accounts, if available. Someone can easily place physical or software keyloggers to get your account information on these public computers. See About 2 Step Verification Accounts Help

For a compromised gmail account, go to Having trouble signing in and fill in the account recovery form.

Fix Mail Apps and Devices Show Incorrect Password Error After Enabling 2...
[Fix] Mail Apps and Devices Show Incorrect Password Error After Enabling 2-Step Verification in Microsoft or Gmail Account "2-step verification" is an important security feature which protects your online account whether its your email account or a social networking account. It asks for an extra security code each time you try to sign in to your account. This security code is sent to your registered mobile phone or alternative email ID.
Recently Microsoft enabled this 2-step verification feature for Microsoft accounts which are used for emails, Windows 8, XBox, etc. On the other hand Google is already providing two-step verification in its Gmail service since long time.
If you enabled 2-step verification feature in your Microsoft or Gmail account, you might be facing a weird issue. If you try to access your email account using an email client such as Windows Live Mail, Thunderbird, Microsoft Outlook, etc, it'll now allow you to sign in using your current password. It'll show you an incorrect password error message even if your password is absolutely correct. The same problem will also occur if you try to sign in using your Microsoft account in devices such as Xbox 360 or Android smartphones.
Now the question comes why does this problem occur? Why do these mail apps and devices not accept your correct password? The answer is very simple. These mail apps and devices were not designed to ask you for the extra security code which is required for 2-step verification. Since these apps and devices don't ask for security code, the 2-step verification procedure is not completed successfully, hence you can't sign in using your credentials in those apps and devices.
So what's the solution? The solution is very simple. Every company which provides 2-step verification feature, also allows you to create special passwords for these mail apps and devices. You can create separate passwords for each app and device and then you can use that special password to sign in to those apps or devices. Now those apps and devices will accept the new password and will allow you to access your account without any problem.
So if you have enabled 2-step verification feature in Microsoft or Gmail account and if you are facing login password problems in mail apps or devices, you just need to create above mentioned special passwords or codes to sign in without any problem.
Just follow these simple steps to create app passwords for your Microsoft or Gmail account:

A. Create App Password in Microsoft Account 1. Open your Microsoft account security settings page by clicking on following link:
Open Microsoft Account Security Settings Page
2. You'll see "App passwords" section at the bottom of the page which shows following information:
Some apps and devices don't support security codes. In these cases, you need to create an app password to sign in. 3. Click on "Create a new app password" link and it'll immediately provide you a new password generated randomly.

Now you can use this new password to sign in to a 3rd party mail app or device.
B. Create Application Specific Password in Gmail Account

1. Open your Google account settings page by clicking on following link:
Open Google Account Settings Pag
2. Now click on "Security" tab given in left-side pane. Scroll down on the page and you'll see "Connected applications and sites" section at the bottom of the page.
3. Click on "Manage access" button and it'll open a new page showing following information:Some applications that work outside a browser aren't yet compatible with 2-step verification and cannot ask for verification codes, for example: email programs including Outlook, Apple Mail, or Thunderbird, older Android smartphones. To use these applications, you need to generate an application-specific password. 4. Type any desired name in given text box and click on "Generate password" button.That's it. It'll immediately provide you a new password which can be used in any mail app or device to sign in.PS: If you want to remove or disallow any mail app or device to access your account, you can remove existing app password or revoke access from devices using the same account security settings pages as mentioned in above instructions.

how that helps good luck.

You can combine multiple Gmail accounts into a single, primary Gmail account by using the POP3 Mail Fetcher application built into Gmail.
The Mail Fetcher enables you to retrieve email from POP3 email accounts, including Gmail, and send mail as if from a different email address all from within your primary Gmail account. Configure your primary account to manage your other Gmail accounts with the Mail Fetcher.

Sign in to the Gmail account that you want to use to manage your Gmail accounts.
Click the "Settings" icon, represented by a gear cog, in the top left and click "Mail Settings."

Click the "Accounts and Import" tab.
Click the "Add POP3 Email Account" button.
Enter the email address of your secondary email account and then click "Next Step."
Enter the password of your secondary email account and then click "Add Account."
Click the radio button beside "Yes, I want to be able to send email as
[SECONDARY EMAIL ADDRESS]" and then click "Next Step."
Enter the display name for your secondary email address and then click "Next Step."
Click "Send Verification" and then check your secondary email account.
Click the link contained in the verification email to confirm the integration of that account with your primary Gmail account.
All mail sent to your secondary Gmail is now delivered to your primary account, and when responding your secondary Gmail address is displayed in the From section of the email.

Access all your gmail accounts

There are cople ways to access your account in case of lost/stolen phone:
You have several ways you can get back into your account, depending on your circumstances.
Use backup options
Sign in from a trusted computer
Retrieve code with voicemail and a voice call
Get a new phone from your carrier
Fill out our Account Recovery form

We recommend you use this option only if you cannot get into your account in any other way. This process can take several days and usually involves more effort than other recovery options.

1. Sign in to your account with your username and password.
2. On the verification code challenge page, click Other ways to get a verification code?
3. Click "I no longer have access to any of these."
4. You'll then need to fill out an account recovery form to verify ownership of the account. Take time to answer each question to the best of your ability. The form was designed to ensure that no one can gain access to your account except you. Since Google doesn't collect a lot of information about you when you sign up for an account, we will ask you questions like when you created your account, what Google services you use, and who you email frequently (if you use Gmail) to make certain you are authorized to access your account.

u first ur volume up key+homekey+pwrkey long press.and next reset ur mobile.