What are some marketing strategies that you have used in the past or that have been proven to work well to obtain your competitor's customers and gain more market share?
This is very close to home for me as I spent the last decade developing and advising businesses including Fortune 500 companies on competitive and growth strategies.
Ahead of thinking of the channels; that's easy, ask yourself, why?
Why, would a competitor's customer want my product over theirs?
The best exercise you can do in this case is a SWOT analysis:
You don't have to make it overly academic; look at your strengths and list them all. Then do the same with your weaknesses.
Then repeat the process for your competitors; do some research; look at their product quality, pricing, availability etc...
Then analyse the key elements of the value proposition:
> Product/ service differentiation: e.g. in value, in quality, in design, in exclusivity etc...
> Pricing: more or less than competitors; why?
> Channels: availability, access, speed, ease
Then go through the Opportunities and the Threats.
Identify how you could convince their audience that you have a better deal (avoid price wars unless you have enough market share and cash to ride the storm - this rarely ends well)
Then design your strategy; where, what, how, when
Reach out if you need more help; good luck