Summarize:

If you're using a gas or electric grill, set it to about 350F (177C). If you're using a charcoal grill, build a low fire and wait until you can comfortably hold your hand above the grate for about 6 seconds. To make sure your sausages don't stick to the grill, use a basting brush to cover the links with a small amount of olive oil. If your grates are messy, oil the grill instead by dipping a paper towel in olive oil and brushing it across the grates. Use tongs so you don't burn yourself. If you're using a charcoal grill, set them next to the flame, not directly over it. Make sure the links are not touching so they can cook thoroughly. After every 2 to 3 minutes, turn the sausage links over with tongs. This will keep them from burning. Shorten the amount of time if the venison starts to blacken. Keep your sausages on the grill until they are firm to the touch and deep or golden brown. For most links, this should take between 10 and 20 minutes. To make sure a sausage is safe to eat, use a food thermometer to check the fattest area of the sausage, removing the link once its internal temperature reaches 160F (71C). When your sausages are done, remove them from the grill and let them sit. When they are cool enough to touch, they are ready to serve. Place leftover links in an airtight container and keep them in the fridge for up to 5 days.
Heat your grill to a medium temperature. Brush your sausages or grill gates with olive oil. Put your sausages on the grill. Turn the links over every few minutes. Grill your sausages until they're 160F (71C) inside. Remove and serve your sausages.