Pulling and disposing of it is the safest thing. If I had a bunch of tomato/ potato plants (potatoes are also susceptible) that's what I would do.
However, I'm a backyard gardener with 5 plants. If I noticed blight beginning on one, rather than losing a fifth of my crop, I would try to save it first.
Trying to save it involves:
1) spray all the other tomato/ potato plants with an organic fungicide first to help prevent spread. Organic fungicides include copper sulphate (considered organic, but I don't use it), milk solution, baking soda solution, things with bacillus subtilis (e.g. Serenade), 3% hydrogen peroxide sprayed straight from the bottle. All of these are fungicidal treatments, but all work best used preventatively or at the first signs of infection.
2) remove and dispose of every affected leaf (don't put in compost pile).
3) trim the plants back enough to be sure you have good air circulation
4) water the soil only, in the AM, don't get the leaves wet
5) once the affected leaves are removed spray the rest of the affected plant with one of the above.
Do them in this order, i.e protect the unaffected ones first so you don't risk spreading it around my your touch, tools, sprays, etc. Remove the infected leaves next so you don't risk spreading it with the spray....
You will need to repeat the sprays at least every couple weeks, more if its been raining. It helps to rotate them, use one one time and a different one the next time.
If none of these are working and your plant is getting progressively worse, THEN pull it.