You will want to research journals and magazines that publish in the same genre as the poetry-- really look for things that print similar works.
To begin your research, take a look at the current edition of the book "Writer's Market". It is a fairly comprehensive listing of locations to submit work. Then, head down to your local public library and see if you can track down copies. Make sure it is appropriate or it will be a waste of time and postage to submit.
Each publisher has different submission guidelines, so make sure to research the specifics. Oftentimes, they are now on the web so it's much easier. Most only want you to submit three to five poems in each submission package, and they generally have length guidelines as well.
Do not submit the poems to multiple publications simultaneously unless you specify it in your cover letter and you are sure that the particular publishers accept simultaneous submissions.
For formatting the poems and manuscript, see if you can locate a copy of "Formatting & Submitting Your Manuscript" (which is actually published by the folks at Writer's Market). It's my favorite reference for all sorts of literary queries.
It could take a long time, and be prepared for multiple rejections. But, if you are persistant, you will find homes for your Grandad's poems.
Let me also suggest checking out the website http://www.anotherealm.com/prededitors/... to help you avoid other scams in every aspect of writing.
Another option would be to try and publish a book-length collection of his work.
There are two types of publishing: Tradition and Self-Publishing. You will first need to decide which of these methods you want to pursue. Each has advantages and disadvantages that need to be researched. For instance, traditional publishing can be a very long road, littered with MANY rejections. Self-publishing will guarantee you a printed copy of your book, however you will not see it in a brick-and-mortar bookstore.
http://www.lulu.com is, in my opinion, the best self-publisher around. You can set up your book on their website, for free, and they will print copies as they are purchased. They do not edit your book, so you will need to take care of that on your own. This will also NOT get your book in a traditional bookstore, although you can purchase a very affordable package that would allow sale of your book through online bookstores like Amazon.
"Writer's Market", along with "The Guide to Literary Agents" are my two suggestions for diving into the traditional publishing market. I suggest looking for an agent first because they are the best step through the publishing door. You will create a submission package that matches the agents preferences (some, for instance, just want a query letter and summary in your first contact with them while others want more). Once you find an agent that is willing to represent you, they will market your book to publishers. Remember, in traditional publishing you should not be paying for anything! They get paid when you get paid!
Good luck!