The island can only be reached via the footbridge from the Virginia side, so you'll have to park in the parking lot off of the George Washington Memorial Parkway (northbound only). It is only a few minutes' walk from the Rosslyn Metro station so you can take the DC metro if you prefer. Bicycles are not permitted on the island, so there is a bike rack near the footbridge.
Not far from the footbridge, there's a path that leads to the Theodore Roosevelt Memorial Plaza. The plaza features a large statue of TR and four large monoliths with some of his more famous quotes.
The various landforms on the island make for an interesting and enjoyable walk. There is a boardwalk trail through the swamp/wetlands area which eventually leads to the rocky outcroppings and a nice view of Georgetown.
The island's vegetation is quite diverse for a relatively small area, due to its geological and topographic variety, the frequency of floods, its land-use history (including various periods of landscaping), and its location in an urban area in which many non-native species occur. Most of the island is deciduous forest of various kinds, including uplands, riparian shores, and swamps. There is also an area of fresh-water tidal (estuarine) marsh, and a few small bedrock outcrops of metamorphic Piedmont rock, some along the tidal shore. The variety of freshwater estuarine intertidal habitats along the island's shores is particularly notable.