Don't do that. Ever.
Firstly, why should your client pay for you to teach yourselves? Secondly, you could screw over their website then they'd have to pay someone, like me, more money to fix things.
If you seriously want to get into it, and it's not just because everyone else is doing it and you think you can earn a lot of money, then buy domains yourself, build websites and practice on them. Don't **** around with someones business. Especially if they're paying you.
How do you go about getting into it? You need to learn more than the basics before you consider offering SEO as a service. You need to understand how search engines work, how they crawl, why they crawl, what they see, how they work out keywords, how they look at the value of links, how the determine relevancy. Then you need to look at link building, content creation, how to up someones conversion rate, how to map good internal linking blah blah blah blah.
Also, and this is coming from a freelance SEO, it would take a long while for me to teach you everything that we know. It's not something that can be condensed into 2 months of work. I've spent just under 4 years building up my experience and knowledge and I still know I'm not going to be winning awards anytime soon.
Your current options are:
Say no, offer them the number of somebody trusted and leave it at that.
Start to practice and learn. It won't happen over night and it's going to be a long and hard process but if you're committed, you'll learn. Still say no, pass on number of a good SEO.
Team up with an SEO and work on a white label basis. The SEO will provide your client the work under the name of your company. This way, you can earn a bit of cash and keep everything under one roof.
Expand and look for a third partner who has great online marketing knowledge.
Practice on somebodys website who is paying you money based on good faith and you **** it all up
Basically, what i'm saying is you need to learn, absorb, practice and enjoy it! But never use a clients website to test things. Thats a big, bad no!
I'm not trying to be all "my precious" about SEO. It's just see every web design company thinking they can offer amazing services because they know how to put keywords into a website. Or they boast about ranking a ****ty website for a keyword that has never been searched before and I don't want you guys thinking it's just a nice little earner without much output. If you're completely new to the industry, you might think you know a lot, but believe me, you won't.