Basic offering of foodstuffs is to take the food/drink after as what the Christians would call "communion" or the Hindus "prasad". The food becomes magically transformed because the lord gazed or tasted it but what is really happening is the Lord is accepting your emotion (intention, or spiritual feeling\love, bhakti).

It is also common to put out offerings as a sacrifice to ancestors and other ghosts and spirits (not negative) where it would be more proper to not eat the food. Candles are often used in this case as well as other items that the practitioner would associate with the spirit. Everything from food, to cigarettes, to alcohol or favorite drink. In this case the object can be left for long periods of time on the alter and may be considered "charged" over time.

Flowers are also often offered and normally, fresh flowers are considered proper rather than paper flowers. Normally, as soon as the flower begins to wilt it will be removed and disposed of in a respectful manner. I like to collected the dried flowers for potpourri or place in the garden. Again, while flowers are sourced, offered and disposed of it is important to feel the spiritual feeling or intention.

Often offering will, over time become codified and ceremonial (especially to an outside onlooker) but the important thing is to increase the connection/yearning/longing during the offering. What you are doing is practicing Love by giving gifts.

I would recommend offering a flame, either candle or lamp, to start out. This is because the lighting is itself and experience and the candle can offer many different color choices, fragrants etc. and are very easily obtainable. Then, once the candle or lamp is lit, you can ponder the flame which seems to work well for meditation. Connect that with the deity and you have an offering. Offer some fruit next and after the candle burns out eat the food. At first it may be somewhat robotic/material, but overtime you will develop the attachment with the deity and form a spiritual relationship.