Short answer
In Gmail, open Settings, See all settings, General, Signature, create a new one, paste it and save. In Outlook, go to Settings, Accounts, Signatures, then paste and save. The free email signature generator on this site builds one you can copy and paste, with a logo if you want.
Free tools for this
Write the signature first
Build it in the free email signature generator, pick a layout, add your details and click Copy signature. Keep it short: name, role, one or two ways to reach you, a website and a few links. Long quotes and big banners slow email down and often land in spam.
Gmail
Click the gear, then See all settings. On the General tab, scroll to Signature and choose Create new. Paste the signature, then scroll to the bottom and click Save changes. Choose it as the default for new emails and replies if you want it on every message.
Try it now: Email Signature Generator → · Email Deliverability Check →
Outlook on the web and the new Outlook
Open Settings, then Accounts, then Signatures. Choose New signature, paste it in, and set it as the default for new messages and replies. Click Save.
Outlook for desktop
Go to File, Options, Mail, Signatures, then New. Name it, paste it into the editing box and click OK. Set which account and which messages it applies to.
Apple Mail and phones
Apple Mail lets you paste a signature under Mail, Settings, Signatures, but rich layouts can lose their formatting there, so send a test to yourself.
Phone apps often have their own signature setting and many keep it plain text. Check the app's settings and, if needed, use the plain text version.
Putting a logo or photo in
The picture has to be on the web, with an address you can paste. Email apps cannot show a file that only lives on your computer. Your own website or store is the safest home for it.
Use PNG or JPG. Some email apps, Outlook especially, may not show WebP. Make the picture about twice the size it appears at so it stays sharp on phones.
Test it
Send a signed email to yourself and to a friend with a different email app. Open it on your phone. Check the links work and the layout has not shifted.