Summarize the following:
Under your avatar on the right, select Settings from the gear menu. In the Settings window, choose the Accounts and Import link from the menu across the top. In the Accounts and Import window, in the second column, click on the Import mail and contacts link. In the resulting window, "Step 1: sign into your other email account," enter the email account associated with your Hotmail. In the next window, enter the password associated with your Hotmail account: Select the options you wish to include when importing from Hotmail into Gmail. You can choose to import only your email, your email and contacts, or add extra options, as shown. When you've selected the desired options, click Start import. It can take a while to import all your information, especially if you have a lot email and contacts. When it's finished, you're good to go! Note: this method works for other email providers. To see a full list of providers that Google can import, as wall as learning more about switching to Gmail, click here.

Summary:
Open Gmail. Choose Accounts and Import. Choose "Import mail and contacts". Enter the address of your Hotmail account. Enter your Hotmail password. Choose your import options. Be patient.