The pronunciation of Old English wasn't so different from that of contemporary English. However, there were a few notable differences in the pronunciation of consonants and vowels. Let's look at a few.
The /r/ of Old English was a trill, a sound that we hear in languages such as Spanish and Russian. Though this sound can be heard in varieties, i.e., Scottish English, it isn't so common in the English of today. Most English speakers now use a sound that isn't so common in the languages of the world.
Old English had long vowels and consonants. Though modern English also has short and long vowels such as in sit and seat, the short and long vowels of Old English were quantitative. The difference was not in the quality of the vowel sound but in the length.
Old English had a vowel which no longer exists in English. This was the front vowel heard in the French word lune (moon). It is pronounced with rounded lips.
Old English also had long consonants. Modern English no longer does. In the word apple, the double p is pronounced as a short consonant. In Old English, such a consonant was pronounced long. Languages which have long consonants include Italian and Swedish.
With respect to pronunciation, English hasn't changed so much over the years. The spelling has changed much more. The main differences were that Old English had qualitative short and long vowels, long consonants, a front vowel that no longer exists and an /r/ that was pronounced as a trill.