It can be tough, very much so.

Firstly, I’d recommend trying to maintain a somewhat consistent schedule, and try for at least one update a week.  Not everyone can be Wiggles and pull off 3 multi-paneled updates a week while maintaining an actual life, but consistency is still important and can help stave off art block.

Don’t dive straight into a story.  Take some time and get used to things before getting invested in a storyline for your blog.  A story from the start can work, and has for many people, but it can also make you feel locked in to a formula and make you follow ideas that at first seem brilliant, but you can later come to loathe.

Start the ask blog on a separate account, not a side blog.  One of the most enjoyable aspects of an ask blog is the interaction, both between your followers and you, and between you and those you follow.  Starting an ask blog on its own account and being able to send questions as your character not only helps you to establish the character, but also to spread the name and image of your blog.  At least for me, I am more likely to follow a blog that pops up on my dashboard if it is an ask blog that updates somewhat frequently and has a good character.  This is especially true for drawn blogs.

If you are starting a drawn ask blog, then take pride in your work, but don’t stress over how good or bad you are.  You can be proud of a stick drawing, and become an absolutely awe inspiring artist faster than you could think with practice.  On the other hand, you could already be an amazing artist, but hate your work, in which case you will never improve.  I would encourage anyone to try and draw their characters, and answer the questions they get through art before text, because it is hard but it is also incredibly rewarding to hear that even one person likes your art, even if that one person is you.

Don’t start the blog expecting to get popular instantly, or to attract the attention of all of the blogs you look up to.  As you said, it can be hard, and it takes time.  You shouldn’t do anything for the sake of popularity, but because you find it fun to do.  If you enjoy working on your blog, and working with your characters, then other people will like it too and people will follow, possibly including those you look up to.

So, take pride in your work, work on your blog consistently and do it because you love it.  Interact with other blogs, but try not to be too pushy or invasive.  It can be rather formulaic, in a sense, but that’s how I’ve tried to run my blogs, and how others have run theirs, to varying degrees of success.