Well, an obvious way to do this, if you haven't already, is to create foreign language versions of your website. Depending on what countries you want to target, making localised language versions of it will boost your traffic 200% from those areas or even more.

Here's a quick guide to how you can get started with that on your own (http://webcertain.com/multilingual-seo.html).

Beyond that, I'd buy click traffic from countries that are not the US and see where they leave. Then solve for that and, as you get stickier in those countries, you'll also do better on SEO.

Finally, I'd look for some social media / web influencers in the market sector that you are in as well as the countries that you're interested in and see if you can get them to guest post / cross post any content to drive content from their users to you to help increase visibility and earn a little precious SEO benefit as well.

Any further questions, let me know. :)

You can use Google search console to set international targeting. That will help. If you are running paid ads you can also designate that your ads are shown only in the countries of your choice.

Several suggestions:
1. Utilize localized language on your site and in advertising. For example, "flashlight" is a word used in the USA, but "torch" is what is used in the UK and many other countries for the same product. Non-USA users may search for products in their own language, so identify the key words that apply to your product or service, make sure you have the correct translation/context and implement into your website and advertising.

2. Look at securing url's that are appropriate for the country(ies) you are targeting. For example, if your current address is xyzcompany.com, and you are targeting France, look to secure xyzcompany.fr as well.

3. Look to obtain visibility in search engines and databanks that are frequented by the country(ies) you are targeting. In the USA, for example, many organizations look to Hoovers for private company information. In Europe, Kompass may be the better resource in which to be found.

Just a few suggestions - hope they help!

One quick tip: set up localised Adwords campaign, doesn't have to be a big budget, has always worked for me.

Are you focused on a specific channel?
Most answers here seem to be focusing on organic search only.

I also agree that localized content will give you a boost. Consider a multi-country / multi lingual strategy where you can target specific geographies. Include ccTLDs as part of it ns srt them up correctly in your Google Search Console, OR, use subdirectories to direct traffic to specific audiences.

1. Create a subdomain, which shows a)the content in the foreign language of the countries you are targeting and b)have the title, heading, H1 tags, H2 tags in the foreign language which match the content of the body of the page.
for example www.France.yourdomain.com . Page will be in French and localized .
On the home page, a 'select country' dropdown should be installed. So each page(s) are in a specific country and all the text as stated above are in that language with keywords and body text which are prooven to be searched for by people in those countries. A translator and a researcher in google keywords will be needed. I know a good source to hire out such freelancers online.
2. Simply duplicate your current pages into the subdomain pages and their respective countries and redo the text on each, for a language and / or country.
3. After the pages are done, submit them each to google webmaster tools as a page to be indexed.
4. Other parts of the page code need to be changed such as default language.
5. Use some social media such as FB and myspace to create back links with the new language keywords within the link itself.
6. Each subdomain will need to be indexed to the Google, Bing and other key engines to a SPECIFIC COUNTRY. NOT Google.com (which is the USA site home). If you want French people to find you, then Google.fr will need to be the pointed google site for that subdomain. NOT the WHOLE website!

I can offer you a lowered call rate to fill you in on the rest of the details, hire sources and some other pointers.
Inquire please. Thanks.