How much time does it take for SEO results to show up (especially in Google)

It depends on how frequently Google indexes the site content. You can use the site:command to find out the indexing pattern.
In case Google is crawling the website in a week or lesser duration, chances are that the changes will be picked up quickly. This will be better if you use One Click from home page for identifying new content for Google. The existing crawl pattern depends majorly on the New content that is being added to the website. It could be:

• New blogs 
• New press release 
• Product updates 
• Other fresh content 

If no new content is being generated on the website, Google sees the site as a “slow update” one and the crawl pattern could be slow, sometimes more than a month. But, here are the ways you can use to signal Google that the site is updated frequently: Building Links - It is good to get new links, as it improves indexing. You can ask your friends, business associates, or an acquaintance with a blog to pass a link to your website. Press Release - Issue a Press Release with judicious links and Google will notice it quickly. Social Mentions - Google considers Tweets and Google+ updates valuable. Home Page - You should rotate the content through the home page of the website. Anything that is just a click away from the home page will get Google’s attention and help the site in getting indexed. Slowly, start training Google to index your website by changing the keywords. Google loves websites, which delivery fresh and timely content to users. You can start off with a weekly update pattern.