Alfred the Great (r.871-899) issued a new legal code for Wessex, that his biographer Asser tells us is based on both the old West Saxon legal code and the laws of Offa of Mercia who ruled about a century earlier. Alfred's code, therefore, gives us a good idea of what a generic "Anglo-Saxon" legal code was.
Justice in Anglo-Saxon England was seen as a community responsibility and organised at the Hundred level. Hundreds are sub-counties, not unlike county level in US states. Hundreds were both administrative and military units, and local courts were held at the Hundred level, presided over by an ealdorman or perhaps a reeve. Trials were carried out in public, and could be by ordeal. It was seen as the responsibility of the community at large to catch wrong-doers, although in the later 9th century, the fyrd militia may have also played a role in the apprehending of fugitives.
Although capital punishment did exist in Anglo-Saxon law, sentences could often be "restorative" rather than punitive, and largely revolved around a system of fines. Murder was no different; the law sets out a series of weregild values which must be paid by killers to the family of their victim, with prices differing between ealdormen, freemen, clergy and slaves. If a slave killed somebody, their owner was obliged to pay the weregild or free the slave, at which point the slave would be liable.
As you might expect, the laws also covered punishment for non-payment. In the event that weregild reparations were not made, Alfred's codex turns matters over to "The Avengers". This doesn't mean that Iron Man and Thor were called in, but rather that if a victim's family was not compensated, then they were then allowed to carry out whatever revenge they saw fit on the perpetrators of the crime, free from legal intervention.
Alfred's law codes can be found in Whitelock's English Historical Documents Vol. I.
Stenton's Anglo-Saxon England and Keynes and Lapidge's Alfred the Great are also useful.