This is a surprisingly tricky question to answer; we have no direct soirces for the experience of fighting in the early medieval west (unlike earlier or later, when people recorded details of battles in texts), and we don't even have artistic depictions of battles from which to reconstruct things like the shield wall. So we're left relying on archaeology, which can tell us a lot, but not as directly as we might prefer.

The principle source of evidence we have about fighting in early sixth-century England are the weapons buried in people's graves. The most common are spears (90% of graves) and shields, with swords being much, much rarer. Interpreting grave goods can be tricky - do the proportions we find in the ground mirror the proportion of weapons used in real life (ie, spears were far more common than swords)? Or were people more likely to bury spears than other weapons for social / symbolic reasons, even though they fought with a much greater variety of weapons? Rather than speculate from a lack of evidence, I personally prefer to go with what we know, and assume that spears were, indeed, the most common choice. This fits with other things we know about sixth-century society: swords require better quality iron than was typically available in the century after the breakdown of the Roman-British economy, and were as a consequence certainly much more valuable, and probably more rare, than comparatively easy-to-make spearheads. From a purely functional perspective as well, the spears that were used in the early sixth century were lighter, more nimble, and better suited for the fast, fluid kind of fighting you might expect to encounter during a cattle raid or border skirmish than the heavy, unbalanced swords we've recovered from contemporary graves (which is not to say that people could not receive devastating wounds from swords - we have examples of truly nasty sword cuts in some persons' graves).

Shields, in this half of the sixth century, seem to have been very small, on the order of 60cm or less in diameter. It's not always easy to determine the precise size of shields in the grave, as the wooden boards rarely leave any traces in British soil, but there are sometimes metal fittings on the edges that show the full diameter of the shield. The pattern is smaller shields in the late fifth century, and large (90ish cm) shields by the seventh, and people buried with weapons circa 500 would be likely to have something toward the smaller end of that range.

These shields could not have been used in a shield wall; they weren't large enough to cover a fighter's upper body or to overlap with one's neighbor. They would have had to be used like later medieval bucklers, as an active rather than passive defense, and suggest that their owners were probably fighting in loose, open skirmishes (again, think rapid cattle raiding, or else small-scale personal defense) rather than organized, close formations like the hoplite phalanx. By the seventh century, we see shields in the ground that would work well in a shield wall, and this perhaps indicates a change in the scale of warfare. But if the weapons we find in early sixth-century graves are an accurate representation of what the living used (a big if, but again: this is all the evidence we have to work from), combat must have been loose and fluid rather than in close ranks. Perhaps, indeed, war involved honor duels and single combat; Guy Halsall has noted that warfare is usually ritualized, and the small shields we find in people's graves would lend themselves well to a kind of fighting that emphasized scripted single combat over massed confrontations.

What about javelins? Most of the spears we find from early sixth-century graves are of a size and shape that would work equally well as a hand-held weapon or a javelin, and I personally hesitate to insist that they be one or the other. It's likely that many weapons were used as both. Occasionally we find a barbed dart which was almost certainly a specialized javelin (perhaps used to pierce and encumber an opponent's shield, like the Roman pilum from which it evolved), but these are comparatively rare in England compared eith the continent. More typically, spearheads from this period had 20-30cm long spearheads with 10-20cm long blades, often this shape, and sometimes with a corrugated or fullered profile to increase stiffness while reducing weight. Spear shafts were narrow (usually c. 2cm), light weight, and about 1.5-2m long. These kinds of spears are easy to throw, and can be incredibly light and nimble in the hand. They're versatile tools.

If we look at weapon injuries on bodies in graves, we get a slightly different picture. The most common wounds are sword cuts to the skull, usually to the front or side of the head (as you'd receive from an opponent in front of you). Spear injuries are comparatively rare. However, this evidence is hampered by poor skeletal preservation: skulls survive better than many other bones, and swords leave wounds that are easier to identify than spear thrusts. So I hesistate to treat this evidence as in any way relresentational, except to say that it shows how nasty a sword cut can be when it connects with a skull.

Finally, I would hesitate to rule out fighting from horseback. It's an old chestnut that Anglo-Saxons always dismounted before figting, but there's no real evidence on which to base this. Horses were sometimes buried in high-status 'warrior' graves from the early sixth century, and there's no reason to believe these animals were purely for transport.

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For further reading, I would recommend starting with Guy Halsall's book Warfare and Society, which provides an excellent overview of the social context of warfare between c. 450-800 CE.

If you have specific questions about anything I've written above, I'm happy to follow up. Most of it is drawn from my own personal research, but I can point you toward archaeological resources to go deeper on your own.

(Edit: corrected a measurement from inches to cm)