I had a very rudimentary grasp of Dutch after 18 months mostly through just speaking to my mother-in-law and watching Dutch TV.
Then I spent another 18 months doing 3 hours a week evening classes. After that I was proficient enough to have hour long conversations.
I don't find it very similar to English, if anything the similarities makes it worse because they often mean something else. It is very close to German and I can understand some German now. You do spot lots of interesting similarities but everything is backwards for starters, it's "four and twenty" not "twenty four" and "what want you eating?" instead of "what do you want to eat?". So it's kind of similar but you sound really stupid unless you get it in the right order.
I think there's a big difference between making yourself understood and speaking without making errors. I've made a big effort to try to get the accent correct which very few do.