Install Dialup Networking

Check, whether 'Dialup-Networking' is already installed, there should be an icon in 'My Computer':

If not, start in the 'Control-Panel' the 'Add/Remove Programs',
select the tab: 'Windows Setup'.
In the 'Communication' section, select 'Dial-Up Networking':

(you will need your Windows 95 floppies/CD-ROM, so that the additional software can be installed).
If you now check in 'Control-Panel' the 'Network'-applet:

Exactly as if you had installed a new network board, Windows95 has installed in addition to the driver for the 'Network-board' 'Dial-Up Adapter' (which is your modem) the Clients for Microsoft and Netware networks and the NetBEUI and IPX/SPX-protocols.
But the Internet is based on the TCP/IP-protocol, which you should add now:

If you used the 'Dial-Up networking' only for the Internet connection (and not also to dial into your office-computer), you should now delete the 'Client for Netware Networks' and the 'NetBEUI' and IPX/SPX-protocols (they do nothing and just 'eat' up memory) but keep the 'Client for Microsoft Networks' (required for Password-Caching), so that your network- configuration should look like:

You need now to configure the TCP/IP-protocol. You could define now the values for your Internet Service Provider (ISP), but I prefer to define them as part of the Dial-Up connection (see later), so we leave the TCP/IP-parameters on its default values:

Since we have installed a Network component, we need to select type method of Logon validation: Primary Network Logon:

A Logon will present you during bootup with a Logon screen, asking you for a Username and (optional) a Password.

If you are ONLY using Dialup Networking without any other Network board,
then you should select as Primary Network Logon: "Windows Logon".
On exiting the Network-applet, you are required to reboot.
You will then get the "Windows Logon" screen:

Enter your name, BUT DO NOT ENTER A PASSWORD, then just OK:

Each time a new Username has been entered, you are asked to confirm the password.
Do not enter ANYTHING here, just select OK to continue.

Since we did NOT enter any password, Windows will NOT present us anymore during
booting with the Logon window.
(If you have already defined a password: Avoiding Logon Windows

If you have in addition to Dialup Networking another network board installed,
you should select as Primary Network Login the Client for your Network
(Client for Microsoft Networks in this example, keep the Client for Netware Networks,
if you are connected to a Novell-server).
Regardless, whether you define a password or not, you will be presented on each
reboot with the Network logon screen:

Security Warning:
Are you using a Peer-to-Peer network ?
Do you have File-and-Print Sharing installed ?

Since your computer becomes part of the Internet, as soon as you connect to your ISP,
ANYBODY knowing your IP-address (or anybody simply accessing random such an IP-Address)
can connect to your disk.
Unless it is your explicit intention to share your disk for access via the Internet, protect
your system by verifying the Properties of the TCP/IP bound to the Dialup-Adapter:

Select the tab: Bindings and UNCHECK the Binding to the File-and-Print Sharing,
this will prevent any access via TCP/IP and via the Dialup-Adapter to your disk.