You can try and just generally strengthen the bond, offerings will help. In my experience you have to give if you want to receive.
You can also just in corporate things into your life that remind you of them to help with connecting on a daily level.
For example I have a big print of The birth of Venus over top of my bed, that's a bit of a large example but you can maybe do the same just with colors, quotes, plants, anything that reminds you of them!
generally understanding the Gods you work with helps to know how they can help you, their strong points and stuff they generally don't care for. I always suggest reading about them as much as you can, maybe bring up some of their stories or whatnot while doing magicky things, things that would relate to whatever you're doing!
Get to know the deity through their religious text. Pray to them, present them offerings, communicate through dreamwork, divination, projection, godform rituals, etc. So just generally build a bond with them and figure out what they are all about, what they like and dislike. In doing so you develop a relationship with them. Which makes it easier to come to them and ask for their help. Think of it this way, it'd be rude to go up to a complete stranger and ask them for things. But asking family or friends for help is likely to go much better. Also, it makes you understand who to ask for what. Like there are certain things you might not want to ask a virgin goddess for help with.
You've received some very good suggestions. I'd also suggest reading the book "Devoted to You" by Judy Harrow for an excellent discussion of working with Patron Deities.
Study the myths and legends pertaining to your chosen deity. Learn about their personality. Study any rituals, ceremonies and worship practices you can find. Meditate on the image of your deity and take note of how you feel during it. Then, start off with simple rituals to connect to your deity.
Depends on the Deity. Each God is an individual and likes different things. Read their text to find traditional offerings. Look up their PCPG to find things others have offered them, use divination and ask them what kind of things they like, etc.
as mentioned, it depends on the deity. i would start by researching the deity in question and go with traditional offerings. like a deity associated with cats might enjoy things like cat statues, fish, maybe milk or catnip. a deity associated with the harvest might enjoy seasonal fruit/vegetables. [and of course there's always incense] as you grow closer, you could ask what they would like. or there's observation [i've received good/bad luck after certain offerings, so i usually keep a watchful eye whenever i give a new thing. i also taste before i give unless i'm 100% sure it's good. i gave less than stellar fruit once and i paid for it] other times something might catch your eye and you think 'my deity would like that' this can be the deity calling to you [some people have claimed to hear their deity say 'i want that thing' it really depends on your relationship]
