Here is an online Primer of Old High German. It's not exactly like a modern grammar, but it outlines the phonetic rules that make OHG unique in thorough dryness (so of course I love it!). It also has in later pages useful paradigms of nouns, verbs, etc., again very thorough--a good reference tool. The kicker, though, is that it has in its Appendices lots of fascinating texts in various dialects of OHG, so one can get a great feel for how the language varied region to region.

An Old High German Primer, by Joseph Wright (1906).

Old High German was the language spoken roughly in the areas of middle and southern Germany. It is distinguished from all other Germanic tongues by the High German Consonant Shift, the first substantial systematic phonetic change discovered by modern philologists. Dialects include Bavarian and Alamannic in the South, East Middle German in the area around Erfurt, and Middle and Rhenish Franconian along the Rhine and Moselle Rivers. These last dialects should be distinguished from Old Low Franconian, which is designated as a separate language (mostly because it did not undergo the High Consonant Shift), and is the ancestor of Dutch.

The first texts written OHG date from the 8thCentury. They include what is considered the first German book, the Abrogans, a Latin-German dictionary named after its first entry; the Muspilli, a poem about the end of the world written (along with the Abrogans) in the Bavarian dialect; the famous Hildebrandslied, apparently written in mixed dialects and much disputed by scholars; a West Franconian poem called the Ludwigslied; and a life of Christ written by Otfrid of Weissenburg called Evangelienbuch, written in South Rhenish Franconian dialect.

Finally, the Strassburg Oaths, written in Rhenish Franconian, also contains the oldest extant example of Old French. (It is a treaty between Charlemagne's grandsons.) I've often wondered what language Charlemagne spoke. Surely the language of his people, the Franks, would have been something called "Franconian", but this could either mean Old Low Franconian, or one of the Rhine or Moselle dialects of Old High German. (If Latin had not been adopted by his people and become Old French, would the French today be speaking something like Flemish? Or perhaps something akin to the Rhine dialects of German?)

Anyway, did Charlemagne speak the language of the Franks, or had old French already come into existence? If his grandsons spoke Old French, how long had it been around? Since Old French is practically a form of Late Latin, was it Charlemagne who introduced Latin into use at the court, or perhaps his father Pippin, who himself was on very good terms with the Pope? Either way, it is interesting to contrast the adoption of Old French by the entire Frankish people with the situation in England when the court adopted Norman French but the people held on to Anglo-Saxon. (French is fully a Romance language, but English, for all its French and Latin influence, is still Germanic.) At the very least, it suggests a remarkable unity of mind and purpose among the Franks, and a very strong feeling of identity with the Roman Church.